What are the divisors of 2491?

1, 47, 53, 2491

There is a total of 4 positive divisors.
The sum of these divisors is 2592.
The arithmetic mean is 648.

4 odd divisors

1, 47, 53, 2491

How to compute the divisors of 2491?

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 2491 by each of the numbers from 1 to 2491 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)

2491 / 1 = 2491 (the remainder is 0, so 1 is a divisor of 2491)
2491 / 2 = 1245.5 (the remainder is 1, so 2 is not a divisor of 2491)
2491 / 3 = 830.33333333333 (the remainder is 1, so 3 is not a divisor of 2491)
...
2491 / 2490 = 1.0004016064257 (the remainder is 1, so 2490 is not a divisor of 2491)
2491 / 2491 = 1 (the remainder is 0, so 2491 is a divisor of 2491)

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 2491 (i.e. 49.909918853871). 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 $\frac{N}{d} = D$ )

2491 / 1 = 2491 (the remainder is 0, so 1 and 2491 are divisors of 2491)
2491 / 2 = 1245.5 (the remainder is 1, so 2 is not a divisor of 2491)
2491 / 3 = 830.33333333333 (the remainder is 1, so 3 is not a divisor of 2491)
...
2491 / 48 = 51.895833333333 (the remainder is 43, so 48 is not a divisor of 2491)
2491 / 49 = 50.836734693878 (the remainder is 41, so 49 is not a divisor of 2491)