What are the divisors of 2992?

1, 2, 4, 8, 11, 16, 17, 22, 34, 44, 68, 88, 136, 176, 187, 272, 374, 748, 1496, 2992

There is a total of 20 positive divisors.
The sum of these divisors is 6696.
The arithmetic mean is 334.8.

16 even divisors

2, 4, 8, 16, 22, 34, 44, 68, 88, 136, 176, 272, 374, 748, 1496, 2992

4 odd divisors

1, 11, 17, 187

How to compute the divisors of 2992?

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 2992 by each of the numbers from 1 to 2992 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)

2992 / 1 = 2992 (the remainder is 0, so 1 is a divisor of 2992)
2992 / 2 = 1496 (the remainder is 0, so 2 is a divisor of 2992)
2992 / 3 = 997.33333333333 (the remainder is 1, so 3 is not a divisor of 2992)
...
2992 / 2991 = 1.0003343363424 (the remainder is 1, so 2991 is not a divisor of 2992)
2992 / 2992 = 1 (the remainder is 0, so 2992 is a divisor of 2992)

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 2992 (i.e. 54.699177324709). 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 $\frac{N}{d} = D$ )

2992 / 1 = 2992 (the remainder is 0, so 1 and 2992 are divisors of 2992)
2992 / 2 = 1496 (the remainder is 0, so 2 and 1496 are divisors of 2992)
2992 / 3 = 997.33333333333 (the remainder is 1, so 3 is not a divisor of 2992)
...
2992 / 53 = 56.452830188679 (the remainder is 24, so 53 is not a divisor of 2992)
2992 / 54 = 55.407407407407 (the remainder is 22, so 54 is not a divisor of 2992)