# Divisors of 64

The divisors of 64 are those numbers that completely divide 64 with the remainder zero. In this section, we will discuss about divisors of 64.

#### Highlights of Divisors of 64

• Divisors of 64: 1, 2, 4, 8, 16, 32 and 64
• Negative divisors of 64: -1, -2, -4, -8, -16, -32 and -64
• Prime divisors of 64:
• Number of divisors of 64: 7
• Sum of divisors of 64: 127
• Product of divisors of 64: 87

#### What are Divisors of 64

A number n is a divisor of 64 if $\frac{64}{n}$ is an integer. Note that if 64/n=m is an integer, then both m and n will be the divisors of 64.

To find the divisors of 64, we need to find the numbers n such that 64/n becomes an integer. We have:

 64/1=64 1, 64 are divisors of 64. 64/2=32 2, 32 are divisors of 64 64/4=16 4, 16 are divisors of 64 64/8=8 8 is a divisor of 64

No numbers other than 1, 2, 4, 8, 16, 32, and 64 can divide 64. So we conclude that

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

Thus, the total number of divisors of 64 is seven.

Divisors of 60: The divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

Divisors of 72: The divisors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Divisors of 75: The divisors of 75 are 1, 3, 5, 15, 25, 75.

Divisors of 100: The divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100.

#### Negative Divisors of 64

We know that if m is a divisor of a number, then -m is also a divisor of that number.

As the divisors of 64 are 1, 2, 4, 8, 16, 32 and 64, we can say that:

The negative divisors of 64 are -1, -2, -4, -8, -16, -32 and -64.

#### Prime Divisors of 64

The divisors of 64 are 1, 2, 4, 8, 16, 32 and 64. Among these numbers, only 2 is a prime number. So we obtain that:

The only prime divisor of 64 is 2.

Key Things

The prime factorization of 64 is given below.

64 = 26

(i) By the number of divisors formula, we have that the number of divisors of 64 is

=(6+1)=7.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 64 is

$=\dfrac{2^7-1}{2-1}$

$=\dfrac{128-1}{1}$

$=127$

(iii) By the product of divisors formula, we have that the product of the divisors of 64 is

=64(Number of divisors of 64)/2

=647/2

=87

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