Factors of 64

The factors of 64 are the numbers, that produce the result as 64 when two numbers are multiplied together. Consider an example, the factor pair of 23 is written as (1,23) and (-1,-23). When we multiply the pair of negative factors, the result should give the original number, such as multiplying -1 × -23, then we get the number 23. Thus, we can consider both positive and negative factor pairs of 23. Factor pairs of the number 64 are the whole numbers which could be either positive or negative but not a fraction or decimal number. To find the factors of a number, 64, we will use the factorization method.

Factors of 64

In the factorization method, first take the numbers, 1 and 64 as factors and proceed with finding the other pair of multiples of 64 which gives the results as an original number. To understand this method in a better way, read the article below to find factor 64 in pairs and also the division method to find the prime factors of 64 is discussed.

Pair Factors of 64

To find the factor pairs of 64, multiply the two numbers in a pair to get the original number as 64, such numbers are as follows

If 1 × 64 = 64, then (1, 64) is a pair factor of 64.

2 × 32 = 64, (2, 32) is a pair factor of 64

4 × 16 = 64, then (4, 16) is a pair factor of 64

8 × 8 = 64, (8, 8) is a pair factor of 64

Therefore, the positive pair factors are (1, 64), (2, 32), (4,16) and (8, 8)

To find the negative pair factors of 64, then proceed with the following steps

-1 × -64 = 64, (-1, -64) is a pair factor of 64.

-2 × -32 = 64, (-2, -32) is a pair factor of 64

-4 × -16 = 64, then (-4, -16) is a pair factor of 64

-8 × -8 = 64, (-8, -8) is a pair factor of 64

Therefore, the negative pair factors are  (-1, -64), (-2,-32), (-4, -16) and (-8, -8)

How to calculate the Factors of 64?

Learn the following steps to calculate the factors of 64.

  • First, write the number 64
  • Find the two numbers, which gives the result as 64 under the multiplication, say 2 and 32, such as 2 × 32 = 64.
  • We know that 2 is a prime number which has only two factors, i.e., 1 and the number itself (1 and 2) which cannot be further factorized.
  • 2 = 2 × 1
  • But look at the number 32, which is a composite number but not a prime number and it can be further factorized.
  • 32 can be factorised as 2 x 2 x 2 x 2 x 2 x 1
  • Therefore, the factorization of 64 is written as, 64 = 2 x 2 x 2 × 2 × 2 x 2 x 1
  • Finally, write down all the unique numbers which we can obtain from 2 x 2 x 2 × 2 × 2 x 2 x 1
Factors of 64
1, 2, 4, 8, 16, 32 and 64

Prime Factors of 64 By Division Method

The number 64 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of a number 64.

Step 1: The first step is to divide the number 64 with the smallest prime factor, say 2.

64 ÷ 2 = 32

Step 2: Again divide 32 by 2 and the process goes on.

32 ÷ 2 = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 64 are written as  2 x 2 × 2 x 2 x 2 x 2 or 26, where 2 is a prime number.

It is possible to find the exact number of factors of a number 64 with the help of prime factorisation. The prime factor of the 64 is 26. The exponent in the prime factorisation is 6. When you add the number 1 with the exponent 6, we get 7. i.e.,6 +1 = 7. Therefore, the number 64 has 7 factors.

Stay tuned with BYJU’S to know about factor 64 and the factors and prime factors of other numbers. Download BYJU’S – The Learning App for better experience and clarification and also watch interactive videos.

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