What are the divisors of 1392?

1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 48, 58, 87, 116, 174, 232, 348, 464, 696, 1392

There is a total of 20 positive divisors.
The sum of these divisors is 3720.
The arithmetic mean is 186.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 58, 116, 174, 232, 348, 464, 696, 1392

4 odd divisors

1, 3, 29, 87

How to compute the divisors of 1392?

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 1392 by each of the numbers from 1 to 1392 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)

1392 / 1 = 1392 (the remainder is 0, so 1 is a divisor of 1392)
1392 / 2 = 696 (the remainder is 0, so 2 is a divisor of 1392)
1392 / 3 = 464 (the remainder is 0, so 3 is a divisor of 1392)
...
1392 / 1391 = 1.000718907261 (the remainder is 1, so 1391 is not a divisor of 1392)
1392 / 1392 = 1 (the remainder is 0, so 1392 is a divisor of 1392)

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 1392 (i.e. 37.309516212355). 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 $\frac{N}{d} = D$ )

1392 / 1 = 1392 (the remainder is 0, so 1 and 1392 are divisors of 1392)
1392 / 2 = 696 (the remainder is 0, so 2 and 696 are divisors of 1392)
1392 / 3 = 464 (the remainder is 0, so 3 and 464 are divisors of 1392)
...
1392 / 36 = 38.666666666667 (the remainder is 24, so 36 is not a divisor of 1392)
1392 / 37 = 37.621621621622 (the remainder is 23, so 37 is not a divisor of 1392)