Divisors of 32

The divisors of 32 are those numbers that completely divide 32 without a remainder. In this section, we will discuss about divisors of 32.

Highlights of Divisors of 32

  • Divisors of 32: 1, 2, 4, 8, 16 and 32
  • Negative divisors of 32: -1, -2, -4, -8, -16 and -32
  • Prime divisors of 32: 
  • Number of divisors of 32: 6
  • Sum of divisors of 32: 63
  • Product of divisors of 32: 32

What are Divisors of 32

A number n is a divisor of 32 if $\frac{32}{n}$ is an integer. Note that if 32/n=m is an integer, then both m and n will be the divisors of 32.

To find the divisors of 32, we need to find the numbers n such that 32/n becomes an integer. We have:

32/1=32 1, 32 are divisors of 32.
32/2=16 2, 16 are divisors of 32
32/4=8 4, 8 are divisors of 32

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

The divisors of 32 are:

1, 2, 4, 8, 16 and 32.

Thus, the total number of divisors of 32 is six.

 

Negative Divisors of 32

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

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

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

 

Prime Divisors of 32

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

The only prime divisor of 32 is 2.

 

Key Things

The prime factorization of 32 is given below.

32 = 25

(i) By the number of divisors formula, we have that the number of divisors of 32 is

=(5+1)=6.

(ii) By the sum of divisors formula, we have that the sum of the divisors of 32 is

$=\frac{2^6-1}{2-1}$

$=\frac{64-1}{1}$

$=63$

(iii) By the product of divisors formula, we have that the product of the divisors of 32 is

=32(Number of divisors of 32)/2

=326/2

=323

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