What are the divisors of 1404?

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 108, 117, 156, 234, 351, 468, 702, 1404

There is a total of 24 positive divisors.
The sum of these divisors is 3920.
The arithmetic mean is 163.33333333333.

16 even divisors

2, 4, 6, 12, 18, 26, 36, 52, 54, 78, 108, 156, 234, 468, 702, 1404

8 odd divisors

1, 3, 9, 13, 27, 39, 117, 351

How to compute the divisors of 1404?

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 1404 by each of the numbers from 1 to 1404 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)

1404 / 1 = 1404 (the remainder is 0, so 1 is a divisor of 1404)
1404 / 2 = 702 (the remainder is 0, so 2 is a divisor of 1404)
1404 / 3 = 468 (the remainder is 0, so 3 is a divisor of 1404)
...
1404 / 1403 = 1.0007127583749 (the remainder is 1, so 1403 is not a divisor of 1404)
1404 / 1404 = 1 (the remainder is 0, so 1404 is a divisor of 1404)

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 1404 (i.e. 37.46998799039). 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 $\frac{N}{d} = D$ )

1404 / 1 = 1404 (the remainder is 0, so 1 and 1404 are divisors of 1404)
1404 / 2 = 702 (the remainder is 0, so 2 and 702 are divisors of 1404)
1404 / 3 = 468 (the remainder is 0, so 3 and 468 are divisors of 1404)
...
1404 / 36 = 39 (the remainder is 0, so 36 and 39 are divisors of 1404)
1404 / 37 = 37.945945945946 (the remainder is 35, so 37 is not a divisor of 1404)