Factors – All Factors of a Number

Factors are the numbers that are exactly divisible by the given original number, which means that they divide the original number leaving nothing as a remainder. 

Factors of any number

Figure 1 – Group of 6 students have been divided into 2 groups with 3 student each

The word “Factor” has been derived from the Latin word “faitor” which means creator or doer. The factor is a divisor of a given number. Factors are important because they allow you to break a number down into smaller parts. When two whole numbers are multiplied together, they are regarded as the factors of the resulting product.

For instance, the product of two whole numbers 2 and 3 is given as:

\[ 2 \times 3 = 6 \]

such that 2 and 3 are the factors of 6.

The Factoring technique has so many uses in real life! You can use it to find the factors of something, which will allow you to divide everything into equal parts or maybe in various real-life instances such as when exchanging money or understanding time while on vacation.

Factoring comes up with all kinds of solutions for problems like these which must sound too complex right now but wait until we get more specific about how factored things are and how it is done.

What Are Factors?

Factors are the numbers that divide the other number such that the remaining number is zero.

Factors can be determined using the division or multiplication method. In addition to these two methods, rules of divisibility can also be used to find the factors of any given number. Factors are not only in the form of numbers but they can also be the algebraic expressions dividing another expression equally.

Factors can be positive as well as negative. The negative factors are the same as positive ones with the opposite sign.

To better understand the concept of finding factors, let’s just find the factors of number 8.

8 can be factored as following:

\[ 1 \times 8 = 8 \]

\[ 2 \times 4 = 8 \]

Therefore, 8 can be factored in as 1, 2, 4, and 8 since we have already learned earlier that the negative factors are nothing but positive factors with opposite signs. So the negative factors are -1, -2, -4, and -8.

The product of two negative numbers is always a positive number where 8 is the positive number, so the factors of 8 are given as:

\[ 1, -1, 2, -2, 4, -4, 8, -8 \]

Usually, the positive factors are considered while solving the problems related to factorization.

How To Find the Factors of a Number

To find the factors of any number, follow the steps mentioned below:

Step 1

Perform the prime factorization of the number whose factors are to be determined.

Step 2

Draw a factor tree for the number. All the numbers originating from the new branches are the factors of the given number.

Step 3

Now, multiply any two of the obtained prime factors to find the other factors of the number.

Step 4

Do not repeat the factors in the list.

Let’s solve an example to understand the method better.

For instance, find the factors of 136 using prime factorization.

The prime factorization of 136 is given as:

Factors tree of one thirty six

Figure 2 – Factor tree of 136 using prime factorization

Now, write the prime factors in the exponent form as:

\[ Prime\ Factor\ of\ 136\ = 2 \times 2 \times 2 \times 17 \]

So, the factors of 136 are:

1, 2, 4, 8, 17, 34, 68, and 136.

Here are some important properties of the factors of the number:

  1. The factors of the number are either less than or equal to the given number in magnitude.
  2. If a number is the factor of a given number then its additive inverse will also be the factor of the number.
  3. The total number of factors is always finite.
  4. The factors of a number can neither be in decimal form nor fractions.
  5. The factors can be found by using the multiplication or division method.
  6. Every number has at least two factors i.e. 1 and the number itself.
  7. only 1 and 0 has 1 factor.

There are other methods such as the multiplication and division methods that can be used to determine the factors of the given number.

Let’s explore each of the methods individually for a better understanding of the concept.

Multiplication Method

To find the factors of the number using the multiplication method, follow the steps given below:

Step 1

Express the given number in the form of the product of two whole numbers.

Step 2

Make all the possible pairs that give the number as the product.

Step 3

The whole numbers whose product is equal to the given number are the factors of that number.

For instance, the factors of 36 using the multiplication method are given as:

\[ 1 \times 36 = 36 \]

\[ 2 \times 18 = 36 \]

\[ 3 \times 12 = 36 \]

\[ 4 \times 9 = 36 \]

\[ 6 \times 6 = 36 \]

Therefore, the factors of 36 found using the multiplication method are:

\[ Factors\ of\ 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36 \]

Division Method

To compute the factors of a number using the division method, follow the steps mentioned below:

Step 1

Make a list of numbers less than the given number whose factors are to be found.

Step 2

Divide each number by the given number.

Step 3

The numbers that when divided give zero as the remainder are the factors of the number.

For example, the factors of 8 found using the division method are:

\[ \dfrac{8}{1} = 8,\ r=0 \]

\[ \dfrac{8}{2} = 4,\ r=0 \]

\[ \dfrac{8}{3} = 2,\ r=2 \]

\[ \dfrac{8}{4} = 2,\ r=0 \]

\[ \dfrac{8}{5} = 1,\ r=3 \]

Therefore, the factors of 8 are given as:

\[ Factors\ of\ 8 = 1, 2, 4, 8\]

The factors can be in the form of algebraic expressions as well. The algebraic factors can be found using various techniques such as factoring quadratic expressions or polynomials.

Hence factors and multiples are very important mathematical concepts that are used for solving many problems

Factors of All the Numbers

Below is the list of factors of various numbers. Now, you do not have to worry about finding the factors of various numbers be it simple or complex, the solution is just one click away.

Factors Of -40Factors Of 237Factors Of 495Factors Of 750
Factors Of -48Factors Of 238Factors Of 496Factors Of 751
Factors Of -6Factors Of 239Factors Of 497Factors Of 752
Factors Of 10Factors Of 241Factors Of 498Factors Of 753
Factors Of 100Factors Of 242Factors Of 499Factors Of 754
Factors Of 105Factors Of 243Factors Of 501Factors Of 755
Factors Of 108Factors Of 244Factors Of 502Factors Of 756
Factors Of 11Factors Of 245Factors Of 503Factors Of 757
Factors Of 112Factors Of 246Factors Of 504Factors Of 758
Factors Of 119Factors Of 247Factors Of 505Factors Of 759
Factors Of 12Factors Of 248Factors Of 506Factors Of 760
Factors Of 120Factors Of 249Factors Of 507Factors Of 761
Factors Of 121Factors Of 250Factors Of 508Factors Of 762
Factors Of 125Factors Of 251Factors Of 509Factors Of 763
Factors Of 126Factors Of 253Factors Of 510Factors Of 764
Factors Of 128Factors Of 254Factors Of 511Factors Of 765
Factors Of 13Factors Of 255Factors Of 513Factors Of 766
Factors Of 130Factors Of 256Factors Of 514Factors Of 767
Factors Of 135Factors Of 257Factors Of 515Factors Of 768
Factors Of 136Factors Of 258Factors Of 516Factors Of 769
Factors Of 14Factors Of 259Factors Of 517Factors Of 770
Factors Of 140Factors Of 260Factors Of 518Factors Of 771
Factors Of 144Factors Of 261Factors Of 519Factors Of 772
Factors Of 147Factors Of 262Factors Of 520Factors Of 773
Factors Of 15Factors Of 263Factors Of 521Factors Of 774
Factors Of 150Factors Of 264Factors Of 522Factors Of 775
Factors Of 16Factors Of 265Factors Of 523Factors Of 776
Factors Of 160Factors Of 266Factors Of 524Factors Of 777
Factors Of 162Factors Of 267Factors Of 525Factors Of 778
Factors Of 168Factors Of 268Factors Of 526Factors Of 779
Factors Of 169Factors Of 269Factors Of 527Factors Of 780
Factors Of 17Factors Of 270Factors Of 528Factors Of 781
Factors Of 176Factors Of 271Factors Of 529Factors Of 782
Factors Of 18Factors Of 272Factors Of 530Factors Of 783
Factors Of 180Factors Of 273Factors Of 531Factors Of 784
Factors Of 19Factors Of 274Factors Of 532Factors Of 785
Factors Of 192Factors Of 275Factors Of 533Factors Of 786
Factors Of 196Factors Of 276Factors Of 534Factors Of 787
Factors Of 2Factors Of 277Factors Of 535Factors Of 788
Factors Of 20Factors Of 278Factors Of 536Factors Of 789
Factors Of 200Factors Of 279Factors Of 537Factors Of 790
Factors Of 210Factors Of 280Factors Of 538Factors Of 791
Factors Of 216Factors Of 281Factors Of 539Factors Of 792
Factors Of 22Factors Of 282Factors Of 540Factors Of 793
Factors Of 224Factors Of 283Factors Of 541Factors Of 794
Factors Of 225Factors Of 284Factors Of 542Factors Of 795
Factors Of 23Factors Of 285Factors Of 543Factors Of 796
Factors Of 24Factors Of 286Factors Of 544Factors Of 797
Factors Of 240Factors Of 288Factors Of 545Factors Of 798
Factors Of 25Factors Of 290Factors Of 546Factors Of 799
Factors Of 252Factors Of 291Factors Of 547Factors Of 800
Factors Of 26Factors Of 292Factors Of 548Factors Of 801
Factors Of 27Factors Of 293Factors Of 549Factors Of 802
Factors Of 28Factors Of 294Factors Of 550Factors Of 803
Factors Of 289Factors Of 295Factors Of 551Factors Of 804
Factors Of 29Factors Of 296Factors Of 552Factors Of 805
Factors Of 3Factors Of 297Factors Of 553Factors Of 806
Factors Of 30Factors Of 298Factors Of 554Factors Of 807
Factors Of 300Factors Of 299Factors Of 555Factors Of 808
Factors Of 31Factors Of 301Factors Of 556Factors Of 809
Factors Of 32Factors Of 302Factors Of 557Factors Of 810
Factors Of 33Factors Of 303Factors Of 558Factors Of 811
Factors Of 336Factors Of 304Factors Of 559Factors Of 812
Factors Of 34Factors Of 305Factors Of 560Factors Of 813
Factors Of 35Factors Of 306Factors Of 561Factors Of 814
Factors Of 36Factors Of 307Factors Of 562Factors Of 815
Factors Of 37Factors Of 308Factors Of 563Factors Of 816
Factors Of 38Factors Of 309Factors Of 564Factors Of 817
Factors Of 384Factors Of 310Factors Of 565Factors Of 818
Factors Of 39Factors Of 311Factors Of 566Factors Of 819
Factors Of 4Factors Of 312Factors Of 567Factors Of 820
Factors Of 40Factors Of 313Factors Of 568Factors Of 821
Factors Of 41Factors Of 314Factors Of 569Factors Of 822
Factors Of 42Factors Of 315Factors Of 570Factors Of 823
Factors Of 43Factors Of 316Factors Of 571Factors Of 824
Factors Of 432Factors Of 317Factors Of 572Factors Of 825
Factors Of 44Factors Of 318Factors Of 573Factors Of 826
Factors Of 45Factors Of 319Factors Of 574Factors Of 827
Factors Of 46Factors Of 320Factors Of 575Factors Of 828
Factors Of 47Factors Of 321Factors Of 577Factors Of 829
Factors Of 48Factors Of 322Factors Of 578Factors Of 830
Factors Of 49Factors Of 323Factors Of 579Factors Of 831
Factors Of 5Factors Of 324Factors Of 580Factors Of 832
Factors Of 50Factors Of 325Factors Of 581Factors Of 833
Factors Of 500Factors Of 326Factors Of 582Factors Of 834
Factors Of 51Factors Of 327Factors Of 583Factors Of 835
Factors Of 512Factors Of 328Factors Of 584Factors Of 836
Factors Of 52Factors Of 329Factors Of 585Factors Of 837
Factors Of 53Factors Of 287Factors Of 586Factors Of 838
Factors Of 54Factors Of 331Factors Of 587Factors Of 839
Factors Of 55Factors Of 332Factors Of 588Factors Of 840
Factors Of 56Factors Of 333Factors Of 589Factors Of 841
Factors Of 57Factors Of 334Factors Of 590Factors Of 842
Factors Of 576Factors Of 335Factors Of 591Factors Of 843
Factors Of 58Factors Of 337Factors Of 592Factors Of 844
Factors Of 6Factors Of 338Factors Of 593Factors Of 845
Factors Of 60Factors Of 339Factors Of 594Factors Of 846
Factors Of 600Factors Of 340Factors Of 595Factors Of 847
Factors Of 61Factors Of 341Factors Of 596Factors Of 848
Factors Of 62Factors Of 342Factors Of 597Factors Of 849
Factors Of 625Factors Of 343Factors Of 598Factors Of 850
Factors Of 63Factors Of 344Factors Of 599Factors Of 851
Factors Of 64Factors Of 345Factors Of 601Factors Of 852
Factors Of 65Factors Of 346Factors Of 602Factors Of 853
Factors Of 66Factors Of 347Factors Of 603Factors Of 854
Factors Of 67Factors Of 348Factors Of 604Factors Of 855
Factors Of 68Factors Of 349Factors Of 605Factors Of 856
Factors Of 69Factors Of 350Factors Of 606Factors Of 857
Factors Of 7Factors Of 351Factors Of 607Factors Of 858
Factors Of 70Factors Of 352Factors Of 608Factors Of 859
Factors Of 72Factors Of 353Factors Of 609Factors Of 860
Factors Of 73Factors Of 354Factors Of 610Factors Of 861
Factors Of 74Factors Of 355Factors Of 611Factors Of 862
Factors Of 75Factors Of 356Factors Of 612Factors Of 863
Factors Of 76Factors Of 357Factors Of 613Factors Of 864
Factors Of 77Factors Of 358Factors Of 614Factors Of 865
Factors Of 78Factors Of 359Factors Of 615Factors Of 866
Factors Of 8Factors Of 360Factors Of 616Factors Of 867
Factors Of 80Factors Of 361Factors Of 617Factors Of 868
Factors Of 81Factors Of 362Factors Of 618Factors Of 869
Factors Of 83Factors Of 363Factors Of 619Factors Of 870
Factors Of 84Factors Of 364Factors Of 620Factors Of 871
Factors Of 85Factors Of 365Factors Of 621Factors Of 872
Factors Of 87Factors Of 366Factors Of 622Factors Of 873
Factors Of 88Factors Of 367Factors Of 623Factors Of 874
Factors Of 89Factors Of 368Factors Of 624Factors Of 875
Factors Of 9Factors Of 369Factors Of 626Factors Of 876
Factors Of 90Factors Of 370Factors Of 627Factors Of 877
Factors Of 900Factors Of 371Factors Of 628Factors Of 878
Factors Of 91Factors Of 372Factors Of 629Factors Of 879
Factors Of 93Factors Of 373Factors Of 630Factors Of 880
Factors Of 94Factors Of 374Factors Of 631Factors Of 881
Factors Of 96Factors Of 375Factors Of 632Factors Of 882
Factors Of 98Factors Of 376Factors Of 633Factors Of 883
Factors Of 99Factors Of 377Factors Of 634Factors Of 884
Factors Of 59Factors Of 378Factors Of 635Factors Of 885
Factors Of 92Factors Of 379Factors Of 636Factors Of 886
Factors Of 71Factors Of 380Factors Of 637Factors Of 887
Factors Of 79Factors Of 381Factors Of 638Factors Of 888
Factors Of 82Factors Of 382Factors Of 639Factors Of 889
Factors Of 86Factors Of 383Factors Of 640Factors Of 890
Factors Of 95Factors Of 385Factors Of 641Factors Of 891
Factors Of 97Factors Of 386Factors Of 642Factors Of 892
Factors Of 101Factors Of 387Factors Of 643Factors Of 893
Factors Of 102Factors Of 388Factors Of 644Factors Of 894
Factors Of 103Factors Of 389Factors Of 645Factors Of 895
Factors Of 104Factors Of 390Factors Of 646Factors Of 896
Factors Of 106Factors Of 391Factors Of 647Factors Of 897
Factors Of 107Factors Of 392Factors Of 648Factors Of 898
Factors Of 109Factors Of 393Factors Of 649Factors Of 899
Factors Of 110Factors Of 394Factors Of 650Factors Of 901
Factors Of 111Factors Of 395Factors Of 651Factors Of 902
Factors Of 113Factors Of 396Factors Of 652Factors Of 903
Factors Of 114Factors Of 397Factors Of 653Factors Of 904
Factors Of 115Factors Of 398Factors Of 654Factors Of 905
Factors Of 116Factors Of 399Factors Of 655Factors Of 906
Factors Of 117Factors Of 400Factors Of 656Factors Of 907
Factors Of 118Factors Of 401Factors Of 657Factors Of 908
Factors Of 122Factors Of 402Factors Of 658Factors Of 909
Factors Of 123Factors Of 403Factors Of 659Factors Of 910
Factors Of 124Factors Of 404Factors Of 660Factors Of 911
Factors Of 127Factors Of 405Factors Of 661Factors Of 912
Factors Of 129Factors Of 406Factors Of 662Factors Of 913
Factors Of 131Factors Of 407Factors Of 663Factors Of 914
Factors Of 132Factors Of 408Factors Of 664Factors Of 915
Factors Of 133Factors Of 409Factors Of 665Factors Of 916
Factors Of 134Factors Of 410Factors Of 666Factors Of 917
Factors Of 137Factors Of 411Factors Of 667Factors Of 918
Factors Of 138Factors Of 412Factors Of 668Factors Of 919
Factors Of 139Factors Of 413Factors Of 669Factors Of 920
Factors Of 141Factors Of 414Factors Of 670Factors Of 921
Factors Of 142Factors Of 415Factors Of 671Factors Of 922
Factors Of 143Factors Of 416Factors Of 672Factors Of 923
Factors Of 145Factors Of 417Factors Of 673Factors Of 924
Factors Of 146Factors Of 418Factors Of 674Factors Of 925
Factors Of 148Factors Of 419Factors Of 675Factors Of 926
Factors Of 149Factors Of 420Factors Of 676Factors Of 927
Factors Of 151Factors Of 421Factors Of 677Factors Of 928
Factors Of 152Factors Of 422Factors Of 678Factors Of 929
Factors Of 153Factors Of 423Factors Of 679Factors Of 930
Factors Of 154Factors Of 424Factors Of 680Factors Of 931
Factors Of 155Factors Of 425Factors Of 681Factors Of 932
Factors Of 156Factors Of 426Factors Of 682Factors Of 933
Factors Of 157Factors Of 427Factors Of 683Factors Of 934
Factors Of 158Factors Of 428Factors Of 684Factors Of 935
Factors Of 159Factors Of 429Factors Of 685Factors Of 936
Factors Of 161Factors Of 430Factors Of 686Factors Of 937
Factors Of 163Factors Of 431Factors Of 687Factors Of 938
Factors Of 164Factors Of 433Factors Of 688Factors Of 939
Factors Of 165Factors Of 434Factors Of 689Factors Of 940
Factors Of 166Factors Of 435Factors Of 690Factors Of 941
Factors Of 167Factors Of 436Factors Of 691Factors Of 942
Factors Of 170Factors Of 437Factors Of 692Factors Of 943
Factors Of 171Factors Of 438Factors Of 693Factors Of 944
Factors Of 172Factors Of 439Factors Of 694Factors Of 945
Factors Of 173Factors Of 440Factors Of 695Factors Of 946
Factors Of 174Factors Of 441Factors Of 696Factors Of 947
Factors Of 175Factors Of 442Factors Of 697Factors Of 948
Factors Of 177Factors Of 443Factors Of 698Factors Of 949
Factors Of 178Factors Of 444Factors Of 699Factors Of 950
Factors Of 179Factors Of 445Factors Of 700Factors Of 951
Factors Of 181Factors Of 446Factors Of 701Factors Of 952
Factors Of 182Factors Of 447Factors Of 702Factors Of 953
Factors Of 183Factors Of 448Factors Of 703Factors Of 954
Factors Of 184Factors Of 449Factors Of 704Factors Of 955
Factors Of 185Factors Of 450Factors Of 705Factors Of 956
Factors Of 186Factors Of 451Factors Of 706Factors Of 957
Factors Of 187Factors Of 452Factors Of 707Factors Of 958
Factors Of 188Factors Of 453Factors Of 708Factors Of 959
Factors Of 189Factors Of 454Factors Of 709Factors Of 960
Factors Of 190Factors Of 455Factors Of 710Factors Of 961
Factors Of 191Factors Of 456Factors Of 711Factors Of 962
Factors Of 193Factors Of 457Factors Of 712Factors Of 963
Factors Of 194Factors Of 458Factors Of 713Factors Of 964
Factors Of 195Factors Of 459Factors Of 714Factors Of 965
Factors Of 197Factors Of 460Factors Of 715Factors Of 966
Factors Of 198Factors Of 461Factors Of 716Factors Of 967
Factors Of 199Factors Of 462Factors Of 717Factors Of 968
Factors Of 201Factors Of 463Factors Of 718Factors Of 969
Factors Of 202Factors Of 464Factors Of 719Factors Of 970
Factors Of 203Factors Of 465Factors Of 720Factors Of 971
Factors Of 204Factors Of 466Factors Of 721Factors Of 972
Factors Of 205Factors Of 467Factors Of 722Factors Of 973
Factors Of 206Factors Of 468Factors Of 723Factors Of 974
Factors Of 207Factors Of 469Factors Of 724Factors Of 975
Factors Of 208Factors Of 470Factors Of 725Factors Of 976
Factors Of 209Factors Of 471Factors Of 726Factors Of 977
Factors Of 211Factors Of 472Factors Of 727Factors Of 978
Factors Of 212Factors Of 473Factors Of 728Factors Of 979
Factors Of 213Factors Of 474Factors Of 729Factors Of 980
Factors Of 214Factors Of 475Factors Of 730Factors Of 981
Factors Of 215Factors Of 476Factors Of 731Factors Of 982
Factors Of 217Factors Of 477Factors Of 732Factors Of 983
Factors Of 218Factors Of 478Factors Of 733Factors Of 984
Factors Of 219Factors Of 479Factors Of 734Factors Of 985
Factors Of 220Factors Of 480Factors Of 735Factors Of 986
Factors Of 221Factors Of 481Factors Of 736Factors Of 987
Factors Of 222Factors Of 482Factors Of 737Factors Of 988
Factors Of 223Factors Of 483Factors Of 738Factors Of 989
Factors Of 226Factors Of 484Factors Of 739Factors Of 990
Factors Of 227Factors Of 485Factors Of 740Factors Of 991
Factors Of 228Factors Of 486Factors Of 741Factors Of 992
Factors Of 229Factors Of 487Factors Of 742Factors Of 993
Factors Of 230Factors Of 488Factors Of 743Factors Of 994
Factors Of 231Factors Of 489Factors Of 744Factors Of 995
Factors Of 232Factors Of 490Factors Of 745Factors Of 996
Factors Of 233Factors Of 491Factors Of 746Factors Of 997
Factors Of 234Factors Of 492Factors Of 747Factors Of 998
Factors Of 235Factors Of 493Factors Of 748Factors Of 999
Factors Of 236Factors Of 494Factors Of 749Factors Of 1000

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