What are the divisors of 925?

1, 5, 25, 37, 185, 925

There is a total of 6 positive divisors.
The sum of these divisors is 1178.
The arithmetic mean is 196.33333333333.

6 odd divisors

1, 5, 25, 37, 185, 925

How to compute the divisors of 925?

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 925 by each of the numbers from 1 to 925 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)

925 / 1 = 925 (the remainder is 0, so 1 is a divisor of 925)
925 / 2 = 462.5 (the remainder is 1, so 2 is not a divisor of 925)
925 / 3 = 308.33333333333 (the remainder is 1, so 3 is not a divisor of 925)
...
925 / 924 = 1.0010822510823 (the remainder is 1, so 924 is not a divisor of 925)
925 / 925 = 1 (the remainder is 0, so 925 is a divisor of 925)

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 925 (i.e. 30.413812651491). 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 $\frac{N}{d} = D$ )

925 / 1 = 925 (the remainder is 0, so 1 and 925 are divisors of 925)
925 / 2 = 462.5 (the remainder is 1, so 2 is not a divisor of 925)
925 / 3 = 308.33333333333 (the remainder is 1, so 3 is not a divisor of 925)
...
925 / 29 = 31.896551724138 (the remainder is 26, so 29 is not a divisor of 925)
925 / 30 = 30.833333333333 (the remainder is 25, so 30 is not a divisor of 925)