What are the divisors of 3792?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 79, 158, 237, 316, 474, 632, 948, 1264, 1896, 3792

There is a total of 20 positive divisors.
The sum of these divisors is 9920.
The arithmetic mean is 496.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 158, 316, 474, 632, 948, 1264, 1896, 3792

4 odd divisors

1, 3, 79, 237

How to compute the divisors of 3792?

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 3792 by each of the numbers from 1 to 3792 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)

3792 / 1 = 3792 (the remainder is 0, so 1 is a divisor of 3792)
3792 / 2 = 1896 (the remainder is 0, so 2 is a divisor of 3792)
3792 / 3 = 1264 (the remainder is 0, so 3 is a divisor of 3792)
...
3792 / 3791 = 1.0002637826431 (the remainder is 1, so 3791 is not a divisor of 3792)
3792 / 3792 = 1 (the remainder is 0, so 3792 is a divisor of 3792)

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 3792 (i.e. 61.579217273363). 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 $\frac{N}{d} = D$ )

3792 / 1 = 3792 (the remainder is 0, so 1 and 3792 are divisors of 3792)
3792 / 2 = 1896 (the remainder is 0, so 2 and 1896 are divisors of 3792)
3792 / 3 = 1264 (the remainder is 0, so 3 and 1264 are divisors of 3792)
...
3792 / 60 = 63.2 (the remainder is 12, so 60 is not a divisor of 3792)
3792 / 61 = 62.16393442623 (the remainder is 10, so 61 is not a divisor of 3792)