What are the divisors of 5992?

1, 2, 4, 7, 8, 14, 28, 56, 107, 214, 428, 749, 856, 1498, 2996, 5992

There is a total of 16 positive divisors.
The sum of these divisors is 12960.
The arithmetic mean is 810.

12 even divisors

2, 4, 8, 14, 28, 56, 214, 428, 856, 1498, 2996, 5992

4 odd divisors

1, 7, 107, 749

How to compute the divisors of 5992?

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 5992 by each of the numbers from 1 to 5992 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)

5992 / 1 = 5992 (the remainder is 0, so 1 is a divisor of 5992)
5992 / 2 = 2996 (the remainder is 0, so 2 is a divisor of 5992)
5992 / 3 = 1997.3333333333 (the remainder is 1, so 3 is not a divisor of 5992)
...
5992 / 5991 = 1.0001669170422 (the remainder is 1, so 5991 is not a divisor of 5992)
5992 / 5992 = 1 (the remainder is 0, so 5992 is a divisor of 5992)

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 5992 (i.e. 77.408009921455). 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 $\frac{N}{d} = D$ )

5992 / 1 = 5992 (the remainder is 0, so 1 and 5992 are divisors of 5992)
5992 / 2 = 2996 (the remainder is 0, so 2 and 2996 are divisors of 5992)
5992 / 3 = 1997.3333333333 (the remainder is 1, so 3 is not a divisor of 5992)
...
5992 / 76 = 78.842105263158 (the remainder is 64, so 76 is not a divisor of 5992)
5992 / 77 = 77.818181818182 (the remainder is 63, so 77 is not a divisor of 5992)