What are the divisors of 976?

1, 2, 4, 8, 16, 61, 122, 244, 488, 976

There is a total of 10 positive divisors.
The sum of these divisors is 1922.
The arithmetic mean is 192.2.

8 even divisors

2, 4, 8, 16, 122, 244, 488, 976

2 odd divisors

1, 61

How to compute the divisors of 976?

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 976 by each of the numbers from 1 to 976 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)

976 / 1 = 976 (the remainder is 0, so 1 is a divisor of 976)
976 / 2 = 488 (the remainder is 0, so 2 is a divisor of 976)
976 / 3 = 325.33333333333 (the remainder is 1, so 3 is not a divisor of 976)
...
976 / 975 = 1.0010256410256 (the remainder is 1, so 975 is not a divisor of 976)
976 / 976 = 1 (the remainder is 0, so 976 is a divisor of 976)

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 976 (i.e. 31.240998703627). 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 $\frac{N}{d} = D$ )

976 / 1 = 976 (the remainder is 0, so 1 and 976 are divisors of 976)
976 / 2 = 488 (the remainder is 0, so 2 and 488 are divisors of 976)
976 / 3 = 325.33333333333 (the remainder is 1, so 3 is not a divisor of 976)
...
976 / 30 = 32.533333333333 (the remainder is 16, so 30 is not a divisor of 976)
976 / 31 = 31.483870967742 (the remainder is 15, so 31 is not a divisor of 976)