What are the divisors of 425?

1, 5, 17, 25, 85, 425

There is a total of 6 positive divisors.
The sum of these divisors is 558.
The arithmetic mean is 93.

6 odd divisors

1, 5, 17, 25, 85, 425

How to compute the divisors of 425?

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 425 by each of the numbers from 1 to 425 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)

425 / 1 = 425 (the remainder is 0, so 1 is a divisor of 425)
425 / 2 = 212.5 (the remainder is 1, so 2 is not a divisor of 425)
425 / 3 = 141.66666666667 (the remainder is 2, so 3 is not a divisor of 425)
...
425 / 424 = 1.002358490566 (the remainder is 1, so 424 is not a divisor of 425)
425 / 425 = 1 (the remainder is 0, so 425 is a divisor of 425)

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 425 (i.e. 20.615528128088). 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 $\frac{N}{d} = D$ )

425 / 1 = 425 (the remainder is 0, so 1 and 425 are divisors of 425)
425 / 2 = 212.5 (the remainder is 1, so 2 is not a divisor of 425)
425 / 3 = 141.66666666667 (the remainder is 2, so 3 is not a divisor of 425)
...
425 / 19 = 22.368421052632 (the remainder is 7, so 19 is not a divisor of 425)
425 / 20 = 21.25 (the remainder is 5, so 20 is not a divisor of 425)