What are the divisors of 2425?

1, 5, 25, 97, 485, 2425

There is a total of 6 positive divisors.
The sum of these divisors is 3038.
The arithmetic mean is 506.33333333333.

6 odd divisors

1, 5, 25, 97, 485, 2425

How to compute the divisors of 2425?

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 2425 by each of the numbers from 1 to 2425 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)

2425 / 1 = 2425 (the remainder is 0, so 1 is a divisor of 2425)
2425 / 2 = 1212.5 (the remainder is 1, so 2 is not a divisor of 2425)
2425 / 3 = 808.33333333333 (the remainder is 1, so 3 is not a divisor of 2425)
...
2425 / 2424 = 1.0004125412541 (the remainder is 1, so 2424 is not a divisor of 2425)
2425 / 2425 = 1 (the remainder is 0, so 2425 is a divisor of 2425)

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 2425 (i.e. 49.244289008981). 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 $\frac{N}{d} = D$ )

2425 / 1 = 2425 (the remainder is 0, so 1 and 2425 are divisors of 2425)
2425 / 2 = 1212.5 (the remainder is 1, so 2 is not a divisor of 2425)
2425 / 3 = 808.33333333333 (the remainder is 1, so 3 is not a divisor of 2425)
...
2425 / 48 = 50.520833333333 (the remainder is 25, so 48 is not a divisor of 2425)
2425 / 49 = 49.489795918367 (the remainder is 24, so 49 is not a divisor of 2425)