What are the divisors of 635?

1, 5, 127, 635

There is a total of 4 positive divisors.
The sum of these divisors is 768.
The arithmetic mean is 192.

4 odd divisors

1, 5, 127, 635

How to compute the divisors of 635?

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 635 by each of the numbers from 1 to 635 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)

635 / 1 = 635 (the remainder is 0, so 1 is a divisor of 635)
635 / 2 = 317.5 (the remainder is 1, so 2 is not a divisor of 635)
635 / 3 = 211.66666666667 (the remainder is 2, so 3 is not a divisor of 635)
...
635 / 634 = 1.0015772870662 (the remainder is 1, so 634 is not a divisor of 635)
635 / 635 = 1 (the remainder is 0, so 635 is a divisor of 635)

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 635 (i.e. 25.199206336708). 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 $\frac{N}{d} = D$ )

635 / 1 = 635 (the remainder is 0, so 1 and 635 are divisors of 635)
635 / 2 = 317.5 (the remainder is 1, so 2 is not a divisor of 635)
635 / 3 = 211.66666666667 (the remainder is 2, so 3 is not a divisor of 635)
...
635 / 24 = 26.458333333333 (the remainder is 11, so 24 is not a divisor of 635)
635 / 25 = 25.4 (the remainder is 10, so 25 is not a divisor of 635)