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: 2
- Number of divisors of 64: 7
- Sum of divisors of 64: 127
- Product of divisors of 64: 87
What are Divisors of 64
Note that if $\dfrac{64}{n}=m$ is an integer, then by definition of divisors we can say that 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. |
Find the number of divisors of 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.
Sum, Product & Number of Divisors of 64:
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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