What are the divisors of 2532?

1, 2, 3, 4, 6, 12, 211, 422, 633, 844, 1266, 2532

There is a total of 12 positive divisors.
The sum of these divisors is 5936.
The arithmetic mean is 494.66666666667.

8 even divisors

2, 4, 6, 12, 422, 844, 1266, 2532

4 odd divisors

1, 3, 211, 633

How to compute the divisors of 2532?

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 2532 by each of the numbers from 1 to 2532 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)

2532 / 1 = 2532 (the remainder is 0, so 1 is a divisor of 2532)
2532 / 2 = 1266 (the remainder is 0, so 2 is a divisor of 2532)
2532 / 3 = 844 (the remainder is 0, so 3 is a divisor of 2532)
...
2532 / 2531 = 1.0003951007507 (the remainder is 1, so 2531 is not a divisor of 2532)
2532 / 2532 = 1 (the remainder is 0, so 2532 is a divisor of 2532)

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 2532 (i.e. 50.318982501636). 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 $\frac{N}{d} = D$ )

2532 / 1 = 2532 (the remainder is 0, so 1 and 2532 are divisors of 2532)
2532 / 2 = 1266 (the remainder is 0, so 2 and 1266 are divisors of 2532)
2532 / 3 = 844 (the remainder is 0, so 3 and 844 are divisors of 2532)
...
2532 / 49 = 51.673469387755 (the remainder is 33, so 49 is not a divisor of 2532)
2532 / 50 = 50.64 (the remainder is 32, so 50 is not a divisor of 2532)