What are the divisors of 375?

1, 3, 5, 15, 25, 75, 125, 375

There is a total of 8 positive divisors.
The sum of these divisors is 624.
The arithmetic mean is 78.

8 odd divisors

1, 3, 5, 15, 25, 75, 125, 375

How to compute the divisors of 375?

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 375 by each of the numbers from 1 to 375 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)

375 / 1 = 375 (the remainder is 0, so 1 is a divisor of 375)
375 / 2 = 187.5 (the remainder is 1, so 2 is not a divisor of 375)
375 / 3 = 125 (the remainder is 0, so 3 is a divisor of 375)
...
375 / 374 = 1.0026737967914 (the remainder is 1, so 374 is not a divisor of 375)
375 / 375 = 1 (the remainder is 0, so 375 is a divisor of 375)

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 375 (i.e. 19.364916731037). 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 $\frac{N}{d} = D$ )

375 / 1 = 375 (the remainder is 0, so 1 and 375 are divisors of 375)
375 / 2 = 187.5 (the remainder is 1, so 2 is not a divisor of 375)
375 / 3 = 125 (the remainder is 0, so 3 and 125 are divisors of 375)
...
375 / 18 = 20.833333333333 (the remainder is 15, so 18 is not a divisor of 375)
375 / 19 = 19.736842105263 (the remainder is 14, so 19 is not a divisor of 375)