What are the divisors of 6125?

1, 5, 7, 25, 35, 49, 125, 175, 245, 875, 1225, 6125

There is a total of 12 positive divisors.
The sum of these divisors is 8892.
The arithmetic mean is 741.

12 odd divisors

1, 5, 7, 25, 35, 49, 125, 175, 245, 875, 1225, 6125

How to compute the divisors of 6125?

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 6125 by each of the numbers from 1 to 6125 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)

6125 / 1 = 6125 (the remainder is 0, so 1 is a divisor of 6125)
6125 / 2 = 3062.5 (the remainder is 1, so 2 is not a divisor of 6125)
6125 / 3 = 2041.6666666667 (the remainder is 2, so 3 is not a divisor of 6125)
...
6125 / 6124 = 1.000163291966 (the remainder is 1, so 6124 is not a divisor of 6125)
6125 / 6125 = 1 (the remainder is 0, so 6125 is a divisor of 6125)

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 6125 (i.e. 78.262379212493). 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 $\frac{N}{d} = D$ )

6125 / 1 = 6125 (the remainder is 0, so 1 and 6125 are divisors of 6125)
6125 / 2 = 3062.5 (the remainder is 1, so 2 is not a divisor of 6125)
6125 / 3 = 2041.6666666667 (the remainder is 2, so 3 is not a divisor of 6125)
...
6125 / 77 = 79.545454545455 (the remainder is 42, so 77 is not a divisor of 6125)
6125 / 78 = 78.525641025641 (the remainder is 41, so 78 is not a divisor of 6125)