Factors of 8 | How to find Prime Factorization of 8

Factors of 8 are the numbers that can be evenly divided into 8 without leaving a remainder. Its factors are 1, 2, 4, and 8. These numbers can be multiplied together to give the product of 8. For example, 2 multiplied by 4 is equal to 8. They play a significant role in mathematics, as they are essential for prime factorization, finding common factors, and solving various mathematical problems involving division and multiplication.

What are the Factors of 8?

These numbers can be evenly divided into 8 without leaving a remainder.

Factors: 1, 2, 4 and 8
Negative Factors: -1, -2, -4 and -8
Prime Factors: 2
Prime Factorization of 8: 2 × 2 × 2 = 2³
The sum of Factors: 15

Key Points:

Any number’s exact divisor is its factor, which divides the given integer exactly.
Every number has the factor 1 in common.
A number’s factors are never equal to the original value.
The most significant factor is the initial number itself.

How to Calculate the Factors of 8?

8 is an even number and a whole number. Finding the factors of the number 8 is very simple as it is a single-digit integer. To calculate the elements, there are a few methods you can use:

Divisibility method
Prime factorization method
Tree Factorization method

Regardless of the method you choose, the factors of number 8 remain the same: 1, 2, 4, and 8.

Pair Factors of 8

The pair factors of the number 8 are two numbers that, when multiplied together, result in the original number 8. As mentioned, the pair factors of the number 8 can be positive or negative. Following are the 8’s positive and negative pair factors:

Positive Pair Factors of 8:

Positive Factors	Positive Pair Factors
1 × 8	(1, 8)
2 × 4	(2, 4)

Negative Pair Factors of 8:

Negative Factors	Negative Pair Factors
-1 × -8	(-1, -8)
-2 × -4	(-2, -4)

Factors of 8 by Division Method

The division method can be used to find the factors of number 8. Finding the integers that divide 8 perfectly without leaving a remainder is required for the division method, and such integers are regarded as factors of the number 8. Let’s use the division method to find the 8 factors now.

Division	Factor	Remainder
8 ÷ 1	1	0
8 ÷ 2	2	0
8 ÷ 4	4	0
8 ÷ 8	8	0

Prime Factorization of 8

To perform prime factorization of 8, follow these steps:

Start with the number 8.
Begin dividing 8 by the smallest prime number, which is 2.
8 ÷ 2 = 4
Divide the quotient (4) by the smallest prime number again, 2.
4 ÷ 2 = 2
The quotient obtained (2) is a prime number.
Write down all the prime factors obtained in the above steps: 2, 2, and 2.
The prime factorization 8 is expressed as the product of these prime factors: 2 × 2 × 2.

Therefore, the prime factorization of 8 is 2 × 2 × 2.

Tree Factorization of 8:

To create a factor tree for 8, follow these steps:

Start with the number 8 at the top of the tree.
Look for a pair of factors of number 8. The elements 8 are 1, 2, 4, and 8.
Choose a couple of factors that multiply to give 8. In this case, 2 and 4 satisfy this condition.
Write two elements (2 and 4) below the number 8, connected by branches.
Continue to factorize each component separately.
Start with the unit containing 2.
The factors of 2 are 1 and 2, but 2 is already a prime number, so it cannot be factored further.
Move to the branch containing 4.
The factors of 4 are 1, 2, and 4, but 4 is also a prime number and cannot be factored further.
The factor tree is complete when all branches contain prime numbers.
Read the factor tree from the bottom to the top to obtain the prime factorization.
The prime factorization 8 is 2 × 2 × 2, which can be written as 2³.