What are the divisors of 2375?

1, 5, 19, 25, 95, 125, 475, 2375

There is a total of 8 positive divisors.
The sum of these divisors is 3120.
The arithmetic mean is 390.

8 odd divisors

1, 5, 19, 25, 95, 125, 475, 2375

How to compute the divisors of 2375?

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 2375 by each of the numbers from 1 to 2375 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)

2375 / 1 = 2375 (the remainder is 0, so 1 is a divisor of 2375)
2375 / 2 = 1187.5 (the remainder is 1, so 2 is not a divisor of 2375)
2375 / 3 = 791.66666666667 (the remainder is 2, so 3 is not a divisor of 2375)
...
2375 / 2374 = 1.0004212299916 (the remainder is 1, so 2374 is not a divisor of 2375)
2375 / 2375 = 1 (the remainder is 0, so 2375 is a divisor of 2375)

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 2375 (i.e. 48.733971724045). 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 $\frac{N}{d} = D$ )

2375 / 1 = 2375 (the remainder is 0, so 1 and 2375 are divisors of 2375)
2375 / 2 = 1187.5 (the remainder is 1, so 2 is not a divisor of 2375)
2375 / 3 = 791.66666666667 (the remainder is 2, so 3 is not a divisor of 2375)
...
2375 / 47 = 50.531914893617 (the remainder is 25, so 47 is not a divisor of 2375)
2375 / 48 = 49.479166666667 (the remainder is 23, so 48 is not a divisor of 2375)