What are the divisors of 5125?

1, 5, 25, 41, 125, 205, 1025, 5125

There is a total of 8 positive divisors.
The sum of these divisors is 6552.
The arithmetic mean is 819.

8 odd divisors

1, 5, 25, 41, 125, 205, 1025, 5125

How to compute the divisors of 5125?

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 5125 by each of the numbers from 1 to 5125 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)

5125 / 1 = 5125 (the remainder is 0, so 1 is a divisor of 5125)
5125 / 2 = 2562.5 (the remainder is 1, so 2 is not a divisor of 5125)
5125 / 3 = 1708.3333333333 (the remainder is 1, so 3 is not a divisor of 5125)
...
5125 / 5124 = 1.0001951600312 (the remainder is 1, so 5124 is not a divisor of 5125)
5125 / 5125 = 1 (the remainder is 0, so 5125 is a divisor of 5125)

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 5125 (i.e. 71.589105316382). 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 $\frac{N}{d} = D$ )

5125 / 1 = 5125 (the remainder is 0, so 1 and 5125 are divisors of 5125)
5125 / 2 = 2562.5 (the remainder is 1, so 2 is not a divisor of 5125)
5125 / 3 = 1708.3333333333 (the remainder is 1, so 3 is not a divisor of 5125)
...
5125 / 70 = 73.214285714286 (the remainder is 15, so 70 is not a divisor of 5125)
5125 / 71 = 72.183098591549 (the remainder is 13, so 71 is not a divisor of 5125)