What are the divisors of 2492?

1, 2, 4, 7, 14, 28, 89, 178, 356, 623, 1246, 2492

There is a total of 12 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 420.

8 even divisors

2, 4, 14, 28, 178, 356, 1246, 2492

4 odd divisors

1, 7, 89, 623

How to compute the divisors of 2492?

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 2492 by each of the numbers from 1 to 2492 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)

2492 / 1 = 2492 (the remainder is 0, so 1 is a divisor of 2492)
2492 / 2 = 1246 (the remainder is 0, so 2 is a divisor of 2492)
2492 / 3 = 830.66666666667 (the remainder is 2, so 3 is not a divisor of 2492)
...
2492 / 2491 = 1.0004014452027 (the remainder is 1, so 2491 is not a divisor of 2492)
2492 / 2492 = 1 (the remainder is 0, so 2492 is a divisor of 2492)

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 2492 (i.e. 49.919935897395). 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 $\frac{N}{d} = D$ )

2492 / 1 = 2492 (the remainder is 0, so 1 and 2492 are divisors of 2492)
2492 / 2 = 1246 (the remainder is 0, so 2 and 1246 are divisors of 2492)
2492 / 3 = 830.66666666667 (the remainder is 2, so 3 is not a divisor of 2492)
...
2492 / 48 = 51.916666666667 (the remainder is 44, so 48 is not a divisor of 2492)
2492 / 49 = 50.857142857143 (the remainder is 42, so 49 is not a divisor of 2492)