What are the divisors of 5025?

1, 3, 5, 15, 25, 67, 75, 201, 335, 1005, 1675, 5025

There is a total of 12 positive divisors.
The sum of these divisors is 8432.
The arithmetic mean is 702.66666666667.

12 odd divisors

1, 3, 5, 15, 25, 67, 75, 201, 335, 1005, 1675, 5025

How to compute the divisors of 5025?

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 5025 by each of the numbers from 1 to 5025 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)

5025 / 1 = 5025 (the remainder is 0, so 1 is a divisor of 5025)
5025 / 2 = 2512.5 (the remainder is 1, so 2 is not a divisor of 5025)
5025 / 3 = 1675 (the remainder is 0, so 3 is a divisor of 5025)
...
5025 / 5024 = 1.000199044586 (the remainder is 1, so 5024 is not a divisor of 5025)
5025 / 5025 = 1 (the remainder is 0, so 5025 is a divisor of 5025)

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 5025 (i.e. 70.887234393789). 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 $\frac{N}{d} = D$ )

5025 / 1 = 5025 (the remainder is 0, so 1 and 5025 are divisors of 5025)
5025 / 2 = 2512.5 (the remainder is 1, so 2 is not a divisor of 5025)
5025 / 3 = 1675 (the remainder is 0, so 3 and 1675 are divisors of 5025)
...
5025 / 69 = 72.826086956522 (the remainder is 57, so 69 is not a divisor of 5025)
5025 / 70 = 71.785714285714 (the remainder is 55, so 70 is not a divisor of 5025)