What are the divisors of 708?

1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708

There is a total of 12 positive divisors.
The sum of these divisors is 1680.
The arithmetic mean is 140.

8 even divisors

2, 4, 6, 12, 118, 236, 354, 708

4 odd divisors

1, 3, 59, 177

How to compute the divisors of 708?

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 708 by each of the numbers from 1 to 708 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)

708 / 1 = 708 (the remainder is 0, so 1 is a divisor of 708)
708 / 2 = 354 (the remainder is 0, so 2 is a divisor of 708)
708 / 3 = 236 (the remainder is 0, so 3 is a divisor of 708)
...
708 / 707 = 1.001414427157 (the remainder is 1, so 707 is not a divisor of 708)
708 / 708 = 1 (the remainder is 0, so 708 is a divisor of 708)

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 708 (i.e. 26.6082693913). 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 $\frac{N}{d} = D$ )

708 / 1 = 708 (the remainder is 0, so 1 and 708 are divisors of 708)
708 / 2 = 354 (the remainder is 0, so 2 and 354 are divisors of 708)
708 / 3 = 236 (the remainder is 0, so 3 and 236 are divisors of 708)
...
708 / 25 = 28.32 (the remainder is 8, so 25 is not a divisor of 708)
708 / 26 = 27.230769230769 (the remainder is 6, so 26 is not a divisor of 708)