What are the divisors of 992?

1, 2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992

There is a total of 12 positive divisors.
The sum of these divisors is 2016.
The arithmetic mean is 168.

10 even divisors

2, 4, 8, 16, 32, 62, 124, 248, 496, 992

2 odd divisors

1, 31

How to compute the divisors of 992?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 992 by each of the numbers from 1 to 992 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

992 / 1 = 992 (the remainder is 0, so 1 is a divisor of 992)
992 / 2 = 496 (the remainder is 0, so 2 is a divisor of 992)
992 / 3 = 330.66666666667 (the remainder is 2, so 3 is not a divisor of 992)
...
992 / 991 = 1.0010090817356 (the remainder is 1, so 991 is not a divisor of 992)
992 / 992 = 1 (the remainder is 0, so 992 is a divisor of 992)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 992 (i.e. 31.496031496047). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

992 / 1 = 992 (the remainder is 0, so 1 and 992 are divisors of 992)
992 / 2 = 496 (the remainder is 0, so 2 and 496 are divisors of 992)
992 / 3 = 330.66666666667 (the remainder is 2, so 3 is not a divisor of 992)
...
992 / 30 = 33.066666666667 (the remainder is 2, so 30 is not a divisor of 992)
992 / 31 = 32 (the remainder is 0, so 31 and 32 are divisors of 992)