What are the divisors of 9025?

1, 5, 19, 25, 95, 361, 475, 1805, 9025

There is a total of 9 positive divisors.
The sum of these divisors is 11811.
The arithmetic mean is 1312.3333333333.

9 odd divisors

1, 5, 19, 25, 95, 361, 475, 1805, 9025

How to compute the divisors of 9025?

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 9025 by each of the numbers from 1 to 9025 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)

9025 / 1 = 9025 (the remainder is 0, so 1 is a divisor of 9025)
9025 / 2 = 4512.5 (the remainder is 1, so 2 is not a divisor of 9025)
9025 / 3 = 3008.3333333333 (the remainder is 1, so 3 is not a divisor of 9025)
...
9025 / 9024 = 1.0001108156028 (the remainder is 1, so 9024 is not a divisor of 9025)
9025 / 9025 = 1 (the remainder is 0, so 9025 is a divisor of 9025)

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 9025 (i.e. 95). 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 $\frac{N}{d} = D$ )

9025 / 1 = 9025 (the remainder is 0, so 1 and 9025 are divisors of 9025)
9025 / 2 = 4512.5 (the remainder is 1, so 2 is not a divisor of 9025)
9025 / 3 = 3008.3333333333 (the remainder is 1, so 3 is not a divisor of 9025)
...
9025 / 94 = 96.010638297872 (the remainder is 1, so 94 is not a divisor of 9025)
9025 / 95 = 95 (the remainder is 0, so 95 and 95 are divisors of 9025)