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: 2
- Number of divisors of 32: 6
- Sum of divisors of 32: 63
- Product of divisors of 32: 323
What are Divisors of 32
A number n is a divisor of 32 if $\dfrac{32}{n}$ 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.
Video Solution of Divisors of 32:
Sum, Product & Number of Divisors of 32
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
$=\dfrac{2^6-1}{2-1}$
$=\dfrac{64-1}{1}$
$=63$
(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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