Factors of 64

Definition of factors of 64: If a number completely divides 64 without leaving a remainder, then that number is called a factor of 64. Thus, we can say that the factors of 64 are the divisors of 64.

Here, we will learn about the factors of 64 and the prime factors of 64. We have:

• 64 = 2×2×2×2×2×2 =2⁶ is the prime factorization of 64.
• The factors of 64 are 1, 2, 4, 8, 16, 32, and 64.
• The prime factor of 64 is 2 only
• Negative factors of 64 are –1, -2, -4, -8, -16, -32, and –64.

What are the Factors of 64?

Let us write the number 64 multiplicatively in all possible ways. We definitely have:

64 = 1×64 

64 = 2×32

64 = 4×16

64 = 8×8

As there are no other ways we can write 64 multiplicatively, so we will stop right now. So the factors of 64 in pairs are given as follows:

64 = a×b	Factors in Pairs (a,b)
64 = 1×64	(1, 64)
64 = 2×32	(2, 32)
64 = 4×16	(4, 16)
64 = 8×8	(8, 8)

Thus the pair factors of 64 are (1, 64), (2, 32), (4, 16), and (8, 8). As all the numbers appearing in pair factors are the factors of 64, we conclude that

The factors of 64 are: 1, 2, 4, 8, 16, 32, and 64.

Number of Factors of 64

From above we have calculated the factors of 64 which are 1, 2, 4, 8, 16, 32, and 64.

Thus the total number of factors of 64 is seven.

Prime Factors of 64

Note that the factors of 64 are 1, 2, 4, 8, 16, 32, and 64. Among those factors, we observe that only 2 is a prime number as it does not have any proper divisors.

∴ the only prime factor of 64 is 2.

Question: What are the factors of 64?

Video Solution:

How to Find Factors of 64?

Now we will determine the factors of 64 by division method. In this method, we will try to find the numbers that can divide 64 with no remainder. See that

64/1=64 and the remainder is 0.

∴ 1 and 64 are factors of 64.

64/2=32 and the remainder is 0.

∴ 2 and 32 are factors of 64.

64/4=16 and the remainder is 0.

∴ 4 and 16 are factors of 64.

64/8=8 and the remainder is 0.

∴ 8 and 8 are factors of 64. ⇒ 8 is a factor of 64.

Note that no numbers other than the numbers in violet color can divide 64. So the numbers in violet color, that is, 1, 2, 4, 8, 16, 32, and 64 are the complete list of factors of 64.

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Also Read: 

• Basic concepts of factors
• Square root of 64
• Cube root of 64
• Divisors of 64