# Factors of 8

If a number completely divides 8 with the remainder zero, then that number is called a factor of 8. Note that the factors of 8 are 1, 2, 4, and 8. We will learn about the factors of 8 and the prime factors of 8 here.

## Highlights of Factors of 8

• 8=2×2×2 is the prime factorization of 8.
• The factors of 8 are 1, 2, 4, and 8.
• The only prime factor of 8 is 2.
• Negative factors of 8 are –1, -2, -4, and –8.

## What are the factors of 8?

At first, we will find all the factors of 8 by the multiplication method. To do that, we need to write the number 8 multiplicatively in all possible ways. We have:

 8 = 1×8 ∴ 1, 8 are factors of 8 8 = 2×4 ∴ 2, 4 are factors of 8

We can see that it is not possible to express 8 multiplicatively in any other way. So we will stop right now. We have obtained all the factors of 8 which are in brown color.

∴ the factors of 8 are 1, 2, 4, and 8.

As d is a factor of 8 if and only if -d is a factor of 8, we get all the negative factors of 8. They are -1, -2, -4, and -8.

#### Pair Factors of 8

 8 = a×b Factors in Pairs (a,b) 8 = 1×8 (1, 8) 8 = 2×4 (2, 4)

Thus the positive pair factors of 8 are (1, 8) and (2, 4).

To find the negative factors of 8, we will use the following fact: (a, b) is a positive factor of 8 if and only if (-a, -b) is a negative factor of 8. Thus all the negative pair factors of 8 are (-1, -8) and (-2, -4).

## Number of factors of 8

From above we have calculated the factors of which are 1, 2, 4, and 8. Thus the total number of factors of 8 is four.

## Prime Factors of 8

Note that the factors of 8 are 1, 2, 4, and 8. Among those factors, we observe that only 2 is a prime number as 2 does not have any proper divisors.

∴ the only prime factor of 8 is 2.

 Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 16: 1, 2, 4, 8, 16 Factors of 20: 1, 2, 4, 5, 10, 20 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Question: What are the factors of 8?

Video Solution:

## How to find factors of 8?

Now we will determine the factors of 8 by division method. In this method, we will find the numbers that can divide 8 with no remainder. We have:

 8/1=8 and the remainder is 0 ∴ 1 and 8 are factors of 8 8/2=4 and the remainder is 0 ∴ 2 and 4 are factors of 8

Note that no numbers other than the numbers 1, 2, 4, and 8 can divide 8. Thus 1, 2, 4, and 8 are the complete list of factors of 8.

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## FAQs on Factors of 8

Q1: What are the factors of 8?

Ans: The factors of 8 are 1, 2, 4, and 8. These are the positive factors of 8. The negative factors of 8 are -1, -2, -4, and -8.

Q2: Find the sum of the factors of 8.

Ans: The sum of the factors of 8 is 1+2+4+8=15.

Q3: Is 3 a factor of 8?

Ans: No, 3 is not a factor of 8.

Q4: Find the product of factors of 8.

Ans: The product of factors of 8 is 1×2×4×8 = 64.