What are the divisors of 738?

1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738

There is a total of 12 positive divisors.
The sum of these divisors is 1638.
The arithmetic mean is 136.5.

6 even divisors

2, 6, 18, 82, 246, 738

6 odd divisors

1, 3, 9, 41, 123, 369

How to compute the divisors of 738?

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 738 by each of the numbers from 1 to 738 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)

738 / 1 = 738 (the remainder is 0, so 1 is a divisor of 738)
738 / 2 = 369 (the remainder is 0, so 2 is a divisor of 738)
738 / 3 = 246 (the remainder is 0, so 3 is a divisor of 738)
...
738 / 737 = 1.0013568521031 (the remainder is 1, so 737 is not a divisor of 738)
738 / 738 = 1 (the remainder is 0, so 738 is a divisor of 738)

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 738 (i.e. 27.166155414412). 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 $\frac{N}{d} = D$ )

738 / 1 = 738 (the remainder is 0, so 1 and 738 are divisors of 738)
738 / 2 = 369 (the remainder is 0, so 2 and 369 are divisors of 738)
738 / 3 = 246 (the remainder is 0, so 3 and 246 are divisors of 738)
...
738 / 26 = 28.384615384615 (the remainder is 10, so 26 is not a divisor of 738)
738 / 27 = 27.333333333333 (the remainder is 9, so 27 is not a divisor of 738)