What are the divisors of 2507?

1, 23, 109, 2507

There is a total of 4 positive divisors.
The sum of these divisors is 2640.
The arithmetic mean is 660.

4 odd divisors

1, 23, 109, 2507

How to compute the divisors of 2507?

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 2507 by each of the numbers from 1 to 2507 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)

2507 / 1 = 2507 (the remainder is 0, so 1 is a divisor of 2507)
2507 / 2 = 1253.5 (the remainder is 1, so 2 is not a divisor of 2507)
2507 / 3 = 835.66666666667 (the remainder is 2, so 3 is not a divisor of 2507)
...
2507 / 2506 = 1.0003990422985 (the remainder is 1, so 2506 is not a divisor of 2507)
2507 / 2507 = 1 (the remainder is 0, so 2507 is a divisor of 2507)

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 2507 (i.e. 50.06995106848). 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 $\frac{N}{d} = D$ )

2507 / 1 = 2507 (the remainder is 0, so 1 and 2507 are divisors of 2507)
2507 / 2 = 1253.5 (the remainder is 1, so 2 is not a divisor of 2507)
2507 / 3 = 835.66666666667 (the remainder is 2, so 3 is not a divisor of 2507)
...
2507 / 49 = 51.163265306122 (the remainder is 8, so 49 is not a divisor of 2507)
2507 / 50 = 50.14 (the remainder is 7, so 50 is not a divisor of 2507)