What are the divisors of 2475?

1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 165, 225, 275, 495, 825, 2475

There is a total of 18 positive divisors.
The sum of these divisors is 4836.
The arithmetic mean is 268.66666666667.

18 odd divisors

1, 3, 5, 9, 11, 15, 25, 33, 45, 55, 75, 99, 165, 225, 275, 495, 825, 2475

How to compute the divisors of 2475?

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 2475 by each of the numbers from 1 to 2475 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)

2475 / 1 = 2475 (the remainder is 0, so 1 is a divisor of 2475)
2475 / 2 = 1237.5 (the remainder is 1, so 2 is not a divisor of 2475)
2475 / 3 = 825 (the remainder is 0, so 3 is a divisor of 2475)
...
2475 / 2474 = 1.0004042037187 (the remainder is 1, so 2474 is not a divisor of 2475)
2475 / 2475 = 1 (the remainder is 0, so 2475 is a divisor of 2475)

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 2475 (i.e. 49.749371855331). 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 $\frac{N}{d} = D$ )

2475 / 1 = 2475 (the remainder is 0, so 1 and 2475 are divisors of 2475)
2475 / 2 = 1237.5 (the remainder is 1, so 2 is not a divisor of 2475)
2475 / 3 = 825 (the remainder is 0, so 3 and 825 are divisors of 2475)
...
2475 / 48 = 51.5625 (the remainder is 27, so 48 is not a divisor of 2475)
2475 / 49 = 50.510204081633 (the remainder is 25, so 49 is not a divisor of 2475)