What are the divisors of 744?

1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744

There is a total of 16 positive divisors.
The sum of these divisors is 1920.
The arithmetic mean is 120.

12 even divisors

2, 4, 6, 8, 12, 24, 62, 124, 186, 248, 372, 744

4 odd divisors

1, 3, 31, 93

How to compute the divisors of 744?

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 744 by each of the numbers from 1 to 744 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)

744 / 1 = 744 (the remainder is 0, so 1 is a divisor of 744)
744 / 2 = 372 (the remainder is 0, so 2 is a divisor of 744)
744 / 3 = 248 (the remainder is 0, so 3 is a divisor of 744)
...
744 / 743 = 1.0013458950202 (the remainder is 1, so 743 is not a divisor of 744)
744 / 744 = 1 (the remainder is 0, so 744 is a divisor of 744)

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 744 (i.e. 27.276363393972). 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 $\frac{N}{d} = D$ )

744 / 1 = 744 (the remainder is 0, so 1 and 744 are divisors of 744)
744 / 2 = 372 (the remainder is 0, so 2 and 372 are divisors of 744)
744 / 3 = 248 (the remainder is 0, so 3 and 248 are divisors of 744)
...
744 / 26 = 28.615384615385 (the remainder is 16, so 26 is not a divisor of 744)
744 / 27 = 27.555555555556 (the remainder is 15, so 27 is not a divisor of 744)