What are the divisors of 4625?

1, 5, 25, 37, 125, 185, 925, 4625

There is a total of 8 positive divisors.
The sum of these divisors is 5928.
The arithmetic mean is 741.

8 odd divisors

1, 5, 25, 37, 125, 185, 925, 4625

How to compute the divisors of 4625?

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 4625 by each of the numbers from 1 to 4625 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)

4625 / 1 = 4625 (the remainder is 0, so 1 is a divisor of 4625)
4625 / 2 = 2312.5 (the remainder is 1, so 2 is not a divisor of 4625)
4625 / 3 = 1541.6666666667 (the remainder is 2, so 3 is not a divisor of 4625)
...
4625 / 4624 = 1.0002162629758 (the remainder is 1, so 4624 is not a divisor of 4625)
4625 / 4625 = 1 (the remainder is 0, so 4625 is a divisor of 4625)

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 4625 (i.e. 68.007352543677). 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 $\frac{N}{d} = D$ )

4625 / 1 = 4625 (the remainder is 0, so 1 and 4625 are divisors of 4625)
4625 / 2 = 2312.5 (the remainder is 1, so 2 is not a divisor of 4625)
4625 / 3 = 1541.6666666667 (the remainder is 2, so 3 is not a divisor of 4625)
...
4625 / 67 = 69.029850746269 (the remainder is 2, so 67 is not a divisor of 4625)
4625 / 68 = 68.014705882353 (the remainder is 1, so 68 is not a divisor of 4625)