What are the divisors of 736?

1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736

There is a total of 12 positive divisors.
The sum of these divisors is 1512.
The arithmetic mean is 126.

10 even divisors

2, 4, 8, 16, 32, 46, 92, 184, 368, 736

2 odd divisors

1, 23

How to compute the divisors of 736?

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 736 by each of the numbers from 1 to 736 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)

736 / 1 = 736 (the remainder is 0, so 1 is a divisor of 736)
736 / 2 = 368 (the remainder is 0, so 2 is a divisor of 736)
736 / 3 = 245.33333333333 (the remainder is 1, so 3 is not a divisor of 736)
...
736 / 735 = 1.0013605442177 (the remainder is 1, so 735 is not a divisor of 736)
736 / 736 = 1 (the remainder is 0, so 736 is a divisor of 736)

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 736 (i.e. 27.129319932501). 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 $\frac{N}{d} = D$ )

736 / 1 = 736 (the remainder is 0, so 1 and 736 are divisors of 736)
736 / 2 = 368 (the remainder is 0, so 2 and 368 are divisors of 736)
736 / 3 = 245.33333333333 (the remainder is 1, so 3 is not a divisor of 736)
...
736 / 26 = 28.307692307692 (the remainder is 8, so 26 is not a divisor of 736)
736 / 27 = 27.259259259259 (the remainder is 7, so 27 is not a divisor of 736)