What are the divisors of 2500?

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500

There is a total of 15 positive divisors.
The sum of these divisors is 5467.
The arithmetic mean is 364.46666666667.

10 even divisors

2, 4, 10, 20, 50, 100, 250, 500, 1250, 2500

5 odd divisors

1, 5, 25, 125, 625

How to compute the divisors of 2500?

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 2500 by each of the numbers from 1 to 2500 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)

2500 / 1 = 2500 (the remainder is 0, so 1 is a divisor of 2500)
2500 / 2 = 1250 (the remainder is 0, so 2 is a divisor of 2500)
2500 / 3 = 833.33333333333 (the remainder is 1, so 3 is not a divisor of 2500)
...
2500 / 2499 = 1.000400160064 (the remainder is 1, so 2499 is not a divisor of 2500)
2500 / 2500 = 1 (the remainder is 0, so 2500 is a divisor of 2500)

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 2500 (i.e. 50). 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 $\frac{N}{d} = D$ )

2500 / 1 = 2500 (the remainder is 0, so 1 and 2500 are divisors of 2500)
2500 / 2 = 1250 (the remainder is 0, so 2 and 1250 are divisors of 2500)
2500 / 3 = 833.33333333333 (the remainder is 1, so 3 is not a divisor of 2500)
...
2500 / 49 = 51.020408163265 (the remainder is 1, so 49 is not a divisor of 2500)
2500 / 50 = 50 (the remainder is 0, so 50 and 50 are divisors of 2500)