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Factors of 8: Prime Factorization, Methods, Tree, and Examples

Factors of 8 are a set of numbers that evenly divide 8, leaving no remainder. The remainder must be zero. Only then will that whole number will be considered as a factor of 8
Factors of eight

Figure 1 – All possible Factors of 8

\[ \frac{8}{4} = 2 \] From the above equation, you can understand the concept of finding factors by the division method. When we divide 8 by 4, the remainder is zero, which means 4 evenly divides 8. Condition to be a factor is satisfied. As a result, 4 is a factor of 8. When two numbers are multiplied and their product is 8. Those numbers will be known as factors of 8. Factors can also be explained as something that produces the required output.  In this article, we will grasp what are the factors of 8, how to find them, how to make a factor tree, and what are the prime factors of 8. We will also solve some examples by implementing our concept regarding factors.

What Are the Factors of 8?

Factors of 8 are 1, 2, 4, and 8; there are eight total factors of 8. Four represent positive factors, and the other four represent negative factors. Whole numbers added to this list of factors are the numbers that completely divide 8 leaving the remainder zero. A number having more than 2 factors is known as a composite number. 8 is a composite number.

How To Calculate the Factors of 8?

You can calculate the factors of 8 by two different methods: Division Method and Multiplication Method. Now let’s understand how to calculate the factors of a number using the division method. This method takes more time as you have to divide the given number by different numbers but it is not difficult. To find factors of 8, start dividing it by different numbers and check whether the remainder is zero or not. If the remainder is zero, note those numbers under the list of factors of 8. If the remainder is a non-zero drop down the number and divides the given number by the next possible number.  Always start dividing from the smallest number which is one. 1 is a factor of every number because 1 divides every number completely. As a result of the above discussion 1 is a factor of 8. \[\dfrac{8}{1} = 8 \] 8 is an even number, so it will be divisible by 2. \[\dfrac{8}{2} = 4 \] 2 divides 8 evenly and the remainder is also zero, so 2 is a factor of 8. \[\dfrac{24}{3} = 8 \] Divide 8 by 3 \[\dfrac{8}{3} = 2.66 \] When we divide 8 by 3, it results in 2.66, which is a decimal number, and the remainder is 2. Two is a non-zero number, this means 3 is not a factor of 8. Divide 8 by 4 \[\dfrac{8}{4} = 2 \] The remainder is zero, so 4 is a factor of 8. Divide 8 by 6  \[\dfrac{8}{6} = 1.33 \] When we divide 8 by 6, it results in 1.33, which is a decimal number, and the remainder is 2, which is a non-zero number as a result 6 is also not a factor of 8. Now divide 8 by 8  \[\dfrac{8}{8} = 1 \] Every number divides itself fully with the remainder zero. Every number is a factor in itself. From the above calculations, we conclude that the factors of 8 are : Factors of 8 = 1, 2, 4, 8 Negative factors of 8 are: Negative factors of 8 = -1, -2, -4, -8 

Fun Facts

  • 1 is a factor of every number.
  • The greatest factor in the factor list is equal to the number itself.
  • 2 is a factor of every even number.
  • Any number that is greater than 0 and its ending number is 0 has 2, 5, and 10 as its factors.
  • Factors can never be in fractional or decimal form.
  • Factorization is a common way to solve algebraic equations.

Factors of 8 by Prime Factorization

Prime Factorization is a method of multiplying factors of a number that are prime. The product of such multiplication will be equal to the original number. Prime factors are the factors of a number that are divisible by 1 or the number itself.  The algorithm for finding the prime factorization of a number is to start dividing the number by its prime factors. You always have to start dividing by the smallest prime factor. Factors of 8 = 1, 2, 4, 8  By the above list of factors, we pick the prime factors. 1 is not a prime number. We have only the prime number 2. Start by dividing 8 by 2. \[\frac {8}{2}= 4\] Divide it by 2 because 4 is divisible by 2. \[\frac {4}{2}= 2\] Again, divide it by 2. \[\frac {2}{2}= 1\] Now write it in the form of a table. The Prime Factorization of 8 is shown below in figure 1:
Prime factorization of eight

Figure 2 – Prime Factorization of 8

The final step is to multiply all prime factors. The prime factorization of eight can be written as:

2 x 2 x 2 = 8 

The above equation can also be written as: \[ 2^3 = 8 \]

Factor Tree of 8

The factor tree is a way of representing the prime factorization in the form of a tree. The factor tree contains the number at the top that is being divided by its prime factors. After the division number splits into the divisors and the quotients. Initially, we will divide 8 by its prime factor 2.  \[\frac {8}{2}= 4 \] 8 splits into the 2 (divisor) and 4 (quotient). Now 4 will be divided by 2. \[\frac {4}{2}= 2\] 4 will be branched into 2 (divisor) and 2(quotient). The factor tree of 8 is shown below in figure 2:
Factor tree of eight

Figure 3 – Factor Tree of 8

The prime factorization of 8 can be written as:

Prime Factorization

2 x 2 x 2 = 8 

By observing the above equation, we concluded that 8 is a perfect square.

Factors of 8 in Pairs

Factor pairs are a set of factors that produce the original number when multiplied. We can find factors of 8 by the following multiplication:

1 x 8 = 8 

2 x 4 = 8 

The factor pairs of 8 can be written as: (1, 8) (2, 4) A number can have both positive and negative factor pairs. 8 has 2 positive factor pairs. We can find negative factors of 8 by the following multiplication:

-1 x -8 = 8 

-2 x -4 = 8 

The negative factor pair of 8 are:

(-1, -8)

(-2, -4)

Factors of 8 Solved Examples

Let’s solve some examples related to the factors of 8 for a better understanding.

Example 1

List the factors of 8 in descending order, calculate the sum S1 of the middle two factors, and then calculate the product of the first and last factors. Label it as P1. Prove that S1 is greater than P1

Solution

The factors of number 8 are: Factors of 8 = 1, 2, 4, 8  The factors of number 8 in descending order: Factors of 8 in descending order  = 8, 4, 2, 1  As the two middle factors are 4 and 2, their sum is: Sum S1:

 4+ 2 = 6 

As the first and last factor is 8 and 1, their product is: Product P1:

1 x 8 = 8 

From the above calculations, we conclude that S1 is not greater than P1.

Example 2

Kiara baked 8 sugar cookies and 4 chocolate chip cookies for her 2 friends. She wants to divide the cookies equally among her friends. How many oatmeal and chocolate chip cookies will each friend get?

Solution

Total number of sugar cookies= 8 Total number of chocolate chip cookies= 4 Total number of friends= 2 To find out how many sugar and chocolate chip cookies each friend gets, divide the total number of sugar and chocolate chip cookies by 2: Sugar cookies: \[\frac {8}{2}= 4 \] Chocolate chip cookies:  \[\frac {4}{2}= 2 \] As a result of the above calculation, each friend will get 4 sugar and 2 chocolate chip cookies.

Example 3

Find the common factors of 500 and 8.

Solution

Firstly, list the factors of 500 and 8. Factors of 500 are listed below: Factors of 500 = 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500  Factors of 8 are listed below: Factors of 8 = 1, 2, 4, 8  Common factors are a whole number which is the factor of two or more numbers, and they are present in both lists of factors Common factors of 500 and 8 are: Common factors are = 1, 2, 4

Example 4

The following numbers are given to John. He has to find the number, which is not a factor of 8. Help him find the number. 1, 2, 3, 4, 5, 7, 8

Solution

Given list of numbers  = 1, 2, 3, 4, 5, 7, 8  Factors of 8 are listed below: Factors of 8 = 1, 2, 4, 8 So these numbers are not the factors of 8: Not factors of 8 = 3, 5, 7  Images/mathematical drawings are created with GeoGebra. 

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