What are the divisors of 2736?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 36, 38, 48, 57, 72, 76, 114, 144, 152, 171, 228, 304, 342, 456, 684, 912, 1368, 2736

There is a total of 30 positive divisors.
The sum of these divisors is 8060.
The arithmetic mean is 268.66666666667.

24 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 36, 38, 48, 72, 76, 114, 144, 152, 228, 304, 342, 456, 684, 912, 1368, 2736

6 odd divisors

1, 3, 9, 19, 57, 171

How to compute the divisors of 2736?

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 2736 by each of the numbers from 1 to 2736 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)

2736 / 1 = 2736 (the remainder is 0, so 1 is a divisor of 2736)
2736 / 2 = 1368 (the remainder is 0, so 2 is a divisor of 2736)
2736 / 3 = 912 (the remainder is 0, so 3 is a divisor of 2736)
...
2736 / 2735 = 1.000365630713 (the remainder is 1, so 2735 is not a divisor of 2736)
2736 / 2736 = 1 (the remainder is 0, so 2736 is a divisor of 2736)

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 2736 (i.e. 52.306787322488). 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 $\frac{N}{d} = D$ )

2736 / 1 = 2736 (the remainder is 0, so 1 and 2736 are divisors of 2736)
2736 / 2 = 1368 (the remainder is 0, so 2 and 1368 are divisors of 2736)
2736 / 3 = 912 (the remainder is 0, so 3 and 912 are divisors of 2736)
...
2736 / 51 = 53.647058823529 (the remainder is 33, so 51 is not a divisor of 2736)
2736 / 52 = 52.615384615385 (the remainder is 32, so 52 is not a divisor of 2736)