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