What are the divisors of 996?

1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, 996

There is a total of 12 positive divisors.
The sum of these divisors is 2352.
The arithmetic mean is 196.

8 even divisors

2, 4, 6, 12, 166, 332, 498, 996

4 odd divisors

1, 3, 83, 249

How to compute the divisors of 996?

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 996 by each of the numbers from 1 to 996 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)

996 / 1 = 996 (the remainder is 0, so 1 is a divisor of 996)
996 / 2 = 498 (the remainder is 0, so 2 is a divisor of 996)
996 / 3 = 332 (the remainder is 0, so 3 is a divisor of 996)
...
996 / 995 = 1.0010050251256 (the remainder is 1, so 995 is not a divisor of 996)
996 / 996 = 1 (the remainder is 0, so 996 is a divisor of 996)

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 996 (i.e. 31.559467676119). 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 $\frac{N}{d} = D$ )

996 / 1 = 996 (the remainder is 0, so 1 and 996 are divisors of 996)
996 / 2 = 498 (the remainder is 0, so 2 and 498 are divisors of 996)
996 / 3 = 332 (the remainder is 0, so 3 and 332 are divisors of 996)
...
996 / 30 = 33.2 (the remainder is 6, so 30 is not a divisor of 996)
996 / 31 = 32.129032258065 (the remainder is 4, so 31 is not a divisor of 996)