What are the divisors of 3744?

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 24, 26, 32, 36, 39, 48, 52, 72, 78, 96, 104, 117, 144, 156, 208, 234, 288, 312, 416, 468, 624, 936, 1248, 1872, 3744

There is a total of 36 positive divisors.
The sum of these divisors is 11466.
The arithmetic mean is 318.5.

30 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 26, 32, 36, 48, 52, 72, 78, 96, 104, 144, 156, 208, 234, 288, 312, 416, 468, 624, 936, 1248, 1872, 3744

6 odd divisors

1, 3, 9, 13, 39, 117

How to compute the divisors of 3744?

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 3744 by each of the numbers from 1 to 3744 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)

3744 / 1 = 3744 (the remainder is 0, so 1 is a divisor of 3744)
3744 / 2 = 1872 (the remainder is 0, so 2 is a divisor of 3744)
3744 / 3 = 1248 (the remainder is 0, so 3 is a divisor of 3744)
...
3744 / 3743 = 1.0002671653754 (the remainder is 1, so 3743 is not a divisor of 3744)
3744 / 3744 = 1 (the remainder is 0, so 3744 is a divisor of 3744)

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 3744 (i.e. 61.188234163113). 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 $\frac{N}{d} = D$ )

3744 / 1 = 3744 (the remainder is 0, so 1 and 3744 are divisors of 3744)
3744 / 2 = 1872 (the remainder is 0, so 2 and 1872 are divisors of 3744)
3744 / 3 = 1248 (the remainder is 0, so 3 and 1248 are divisors of 3744)
...
3744 / 60 = 62.4 (the remainder is 24, so 60 is not a divisor of 3744)
3744 / 61 = 61.377049180328 (the remainder is 23, so 61 is not a divisor of 3744)