What are the divisors of 2625?

1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 875, 2625

There is a total of 16 positive divisors.
The sum of these divisors is 4992.
The arithmetic mean is 312.

16 odd divisors

1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 875, 2625

How to compute the divisors of 2625?

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 2625 by each of the numbers from 1 to 2625 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)

2625 / 1 = 2625 (the remainder is 0, so 1 is a divisor of 2625)
2625 / 2 = 1312.5 (the remainder is 1, so 2 is not a divisor of 2625)
2625 / 3 = 875 (the remainder is 0, so 3 is a divisor of 2625)
...
2625 / 2624 = 1.000381097561 (the remainder is 1, so 2624 is not a divisor of 2625)
2625 / 2625 = 1 (the remainder is 0, so 2625 is a divisor of 2625)

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 2625 (i.e. 51.234753829798). 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 $\frac{N}{d} = D$ )

2625 / 1 = 2625 (the remainder is 0, so 1 and 2625 are divisors of 2625)
2625 / 2 = 1312.5 (the remainder is 1, so 2 is not a divisor of 2625)
2625 / 3 = 875 (the remainder is 0, so 3 and 875 are divisors of 2625)
...
2625 / 50 = 52.5 (the remainder is 25, so 50 is not a divisor of 2625)
2625 / 51 = 51.470588235294 (the remainder is 24, so 51 is not a divisor of 2625)