What are the divisors of 2524?

1, 2, 4, 631, 1262, 2524

There is a total of 6 positive divisors.
The sum of these divisors is 4424.
The arithmetic mean is 737.33333333333.

4 even divisors

2, 4, 1262, 2524

2 odd divisors

1, 631

How to compute the divisors of 2524?

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 2524 by each of the numbers from 1 to 2524 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)

2524 / 1 = 2524 (the remainder is 0, so 1 is a divisor of 2524)
2524 / 2 = 1262 (the remainder is 0, so 2 is a divisor of 2524)
2524 / 3 = 841.33333333333 (the remainder is 1, so 3 is not a divisor of 2524)
...
2524 / 2523 = 1.0003963535474 (the remainder is 1, so 2523 is not a divisor of 2524)
2524 / 2524 = 1 (the remainder is 0, so 2524 is a divisor of 2524)

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 2524 (i.e. 50.239426748322). 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 $\frac{N}{d} = D$ )

2524 / 1 = 2524 (the remainder is 0, so 1 and 2524 are divisors of 2524)
2524 / 2 = 1262 (the remainder is 0, so 2 and 1262 are divisors of 2524)
2524 / 3 = 841.33333333333 (the remainder is 1, so 3 is not a divisor of 2524)
...
2524 / 49 = 51.510204081633 (the remainder is 25, so 49 is not a divisor of 2524)
2524 / 50 = 50.48 (the remainder is 24, so 50 is not a divisor of 2524)