What are the divisors of 1656?

1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 69, 72, 92, 138, 184, 207, 276, 414, 552, 828, 1656

There is a total of 24 positive divisors.
The sum of these divisors is 4680.
The arithmetic mean is 195.

18 even divisors

2, 4, 6, 8, 12, 18, 24, 36, 46, 72, 92, 138, 184, 276, 414, 552, 828, 1656

6 odd divisors

1, 3, 9, 23, 69, 207

How to compute the divisors of 1656?

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 1656 by each of the numbers from 1 to 1656 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)

1656 / 1 = 1656 (the remainder is 0, so 1 is a divisor of 1656)
1656 / 2 = 828 (the remainder is 0, so 2 is a divisor of 1656)
1656 / 3 = 552 (the remainder is 0, so 3 is a divisor of 1656)
...
1656 / 1655 = 1.0006042296073 (the remainder is 1, so 1655 is not a divisor of 1656)
1656 / 1656 = 1 (the remainder is 0, so 1656 is a divisor of 1656)

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 1656 (i.e. 40.693979898752). 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 $\frac{N}{d} = D$ )

1656 / 1 = 1656 (the remainder is 0, so 1 and 1656 are divisors of 1656)
1656 / 2 = 828 (the remainder is 0, so 2 and 828 are divisors of 1656)
1656 / 3 = 552 (the remainder is 0, so 3 and 552 are divisors of 1656)
...
1656 / 39 = 42.461538461538 (the remainder is 18, so 39 is not a divisor of 1656)
1656 / 40 = 41.4 (the remainder is 16, so 40 is not a divisor of 1656)