What are the divisors of 2544?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 53, 106, 159, 212, 318, 424, 636, 848, 1272, 2544

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, 6, 8, 12, 16, 24, 48, 106, 212, 318, 424, 636, 848, 1272, 2544

4 odd divisors

1, 3, 53, 159

How to compute the divisors of 2544?

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 2544 by each of the numbers from 1 to 2544 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)

2544 / 1 = 2544 (the remainder is 0, so 1 is a divisor of 2544)
2544 / 2 = 1272 (the remainder is 0, so 2 is a divisor of 2544)
2544 / 3 = 848 (the remainder is 0, so 3 is a divisor of 2544)
...
2544 / 2543 = 1.000393236335 (the remainder is 1, so 2543 is not a divisor of 2544)
2544 / 2544 = 1 (the remainder is 0, so 2544 is a divisor of 2544)

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 2544 (i.e. 50.438080851674). 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 $\frac{N}{d} = D$ )

2544 / 1 = 2544 (the remainder is 0, so 1 and 2544 are divisors of 2544)
2544 / 2 = 1272 (the remainder is 0, so 2 and 1272 are divisors of 2544)
2544 / 3 = 848 (the remainder is 0, so 3 and 848 are divisors of 2544)
...
2544 / 49 = 51.918367346939 (the remainder is 45, so 49 is not a divisor of 2544)
2544 / 50 = 50.88 (the remainder is 44, so 50 is not a divisor of 2544)