What are the divisors of 732?

1, 2, 3, 4, 6, 12, 61, 122, 183, 244, 366, 732

There is a total of 12 positive divisors.
The sum of these divisors is 1736.
The arithmetic mean is 144.66666666667.

8 even divisors

2, 4, 6, 12, 122, 244, 366, 732

4 odd divisors

1, 3, 61, 183

How to compute the divisors of 732?

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 732 by each of the numbers from 1 to 732 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)

732 / 1 = 732 (the remainder is 0, so 1 is a divisor of 732)
732 / 2 = 366 (the remainder is 0, so 2 is a divisor of 732)
732 / 3 = 244 (the remainder is 0, so 3 is a divisor of 732)
...
732 / 731 = 1.0013679890561 (the remainder is 1, so 731 is not a divisor of 732)
732 / 732 = 1 (the remainder is 0, so 732 is a divisor of 732)

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 732 (i.e. 27.055498516937). 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 $\frac{N}{d} = D$ )

732 / 1 = 732 (the remainder is 0, so 1 and 732 are divisors of 732)
732 / 2 = 366 (the remainder is 0, so 2 and 366 are divisors of 732)
732 / 3 = 244 (the remainder is 0, so 3 and 244 are divisors of 732)
...
732 / 26 = 28.153846153846 (the remainder is 4, so 26 is not a divisor of 732)
732 / 27 = 27.111111111111 (the remainder is 3, so 27 is not a divisor of 732)