What are the divisors of 984?

1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984

There is a total of 16 positive divisors.
The sum of these divisors is 2520.
The arithmetic mean is 157.5.

12 even divisors

2, 4, 6, 8, 12, 24, 82, 164, 246, 328, 492, 984

4 odd divisors

1, 3, 41, 123

How to compute the divisors of 984?

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 984 by each of the numbers from 1 to 984 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)

984 / 1 = 984 (the remainder is 0, so 1 is a divisor of 984)
984 / 2 = 492 (the remainder is 0, so 2 is a divisor of 984)
984 / 3 = 328 (the remainder is 0, so 3 is a divisor of 984)
...
984 / 983 = 1.001017293998 (the remainder is 1, so 983 is not a divisor of 984)
984 / 984 = 1 (the remainder is 0, so 984 is a divisor of 984)

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 984 (i.e. 31.368774282716). 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 $\frac{N}{d} = D$ )

984 / 1 = 984 (the remainder is 0, so 1 and 984 are divisors of 984)
984 / 2 = 492 (the remainder is 0, so 2 and 492 are divisors of 984)
984 / 3 = 328 (the remainder is 0, so 3 and 328 are divisors of 984)
...
984 / 30 = 32.8 (the remainder is 24, so 30 is not a divisor of 984)
984 / 31 = 31.741935483871 (the remainder is 23, so 31 is not a divisor of 984)