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.

Also Read:

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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