What are the divisors of 2748?

1, 2, 3, 4, 6, 12, 229, 458, 687, 916, 1374, 2748

There is a total of 12 positive divisors.
The sum of these divisors is 6440.
The arithmetic mean is 536.66666666667.

8 even divisors

2, 4, 6, 12, 458, 916, 1374, 2748

4 odd divisors

1, 3, 229, 687

How to compute the divisors of 2748?

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 2748 by each of the numbers from 1 to 2748 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)

2748 / 1 = 2748 (the remainder is 0, so 1 is a divisor of 2748)
2748 / 2 = 1374 (the remainder is 0, so 2 is a divisor of 2748)
2748 / 3 = 916 (the remainder is 0, so 3 is a divisor of 2748)
...
2748 / 2747 = 1.0003640334911 (the remainder is 1, so 2747 is not a divisor of 2748)
2748 / 2748 = 1 (the remainder is 0, so 2748 is a divisor of 2748)

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 2748 (i.e. 52.421369688325). 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 $\frac{N}{d} = D$ )

2748 / 1 = 2748 (the remainder is 0, so 1 and 2748 are divisors of 2748)
2748 / 2 = 1374 (the remainder is 0, so 2 and 1374 are divisors of 2748)
2748 / 3 = 916 (the remainder is 0, so 3 and 916 are divisors of 2748)
...
2748 / 51 = 53.882352941176 (the remainder is 45, so 51 is not a divisor of 2748)
2748 / 52 = 52.846153846154 (the remainder is 44, so 52 is not a divisor of 2748)