What are the divisors of 632?

1, 2, 4, 8, 79, 158, 316, 632

There is a total of 8 positive divisors.
The sum of these divisors is 1200.
The arithmetic mean is 150.

6 even divisors

2, 4, 8, 158, 316, 632

2 odd divisors

1, 79

How to compute the divisors of 632?

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 632 by each of the numbers from 1 to 632 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)

632 / 1 = 632 (the remainder is 0, so 1 is a divisor of 632)
632 / 2 = 316 (the remainder is 0, so 2 is a divisor of 632)
632 / 3 = 210.66666666667 (the remainder is 2, so 3 is not a divisor of 632)
...
632 / 631 = 1.0015847860539 (the remainder is 1, so 631 is not a divisor of 632)
632 / 632 = 1 (the remainder is 0, so 632 is a divisor of 632)

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 632 (i.e. 25.139610179953). 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 $\frac{N}{d} = D$ )

632 / 1 = 632 (the remainder is 0, so 1 and 632 are divisors of 632)
632 / 2 = 316 (the remainder is 0, so 2 and 316 are divisors of 632)
632 / 3 = 210.66666666667 (the remainder is 2, so 3 is not a divisor of 632)
...
632 / 24 = 26.333333333333 (the remainder is 8, so 24 is not a divisor of 632)
632 / 25 = 25.28 (the remainder is 7, so 25 is not a divisor of 632)