What are the divisors of 5976?

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 83, 166, 249, 332, 498, 664, 747, 996, 1494, 1992, 2988, 5976

There is a total of 24 positive divisors.
The sum of these divisors is 16380.
The arithmetic mean is 682.5.

18 even divisors

2, 4, 6, 8, 12, 18, 24, 36, 72, 166, 332, 498, 664, 996, 1494, 1992, 2988, 5976

6 odd divisors

1, 3, 9, 83, 249, 747

How to compute the divisors of 5976?

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 5976 by each of the numbers from 1 to 5976 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)

5976 / 1 = 5976 (the remainder is 0, so 1 is a divisor of 5976)
5976 / 2 = 2988 (the remainder is 0, so 2 is a divisor of 5976)
5976 / 3 = 1992 (the remainder is 0, so 3 is a divisor of 5976)
...
5976 / 5975 = 1.0001673640167 (the remainder is 1, so 5975 is not a divisor of 5976)
5976 / 5976 = 1 (the remainder is 0, so 5976 is a divisor of 5976)

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 5976 (i.e. 77.304592360351). 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 $\frac{N}{d} = D$ )

5976 / 1 = 5976 (the remainder is 0, so 1 and 5976 are divisors of 5976)
5976 / 2 = 2988 (the remainder is 0, so 2 and 2988 are divisors of 5976)
5976 / 3 = 1992 (the remainder is 0, so 3 and 1992 are divisors of 5976)
...
5976 / 76 = 78.631578947368 (the remainder is 48, so 76 is not a divisor of 5976)
5976 / 77 = 77.61038961039 (the remainder is 47, so 77 is not a divisor of 5976)