What are the divisors of 1692?

1, 2, 3, 4, 6, 9, 12, 18, 36, 47, 94, 141, 188, 282, 423, 564, 846, 1692

There is a total of 18 positive divisors.
The sum of these divisors is 4368.
The arithmetic mean is 242.66666666667.

12 even divisors

2, 4, 6, 12, 18, 36, 94, 188, 282, 564, 846, 1692

6 odd divisors

1, 3, 9, 47, 141, 423

How to compute the divisors of 1692?

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 1692 by each of the numbers from 1 to 1692 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)

1692 / 1 = 1692 (the remainder is 0, so 1 is a divisor of 1692)
1692 / 2 = 846 (the remainder is 0, so 2 is a divisor of 1692)
1692 / 3 = 564 (the remainder is 0, so 3 is a divisor of 1692)
...
1692 / 1691 = 1.0005913660556 (the remainder is 1, so 1691 is not a divisor of 1692)
1692 / 1692 = 1 (the remainder is 0, so 1692 is a divisor of 1692)

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 1692 (i.e. 41.133927602406). 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 $\frac{N}{d} = D$ )

1692 / 1 = 1692 (the remainder is 0, so 1 and 1692 are divisors of 1692)
1692 / 2 = 846 (the remainder is 0, so 2 and 846 are divisors of 1692)
1692 / 3 = 564 (the remainder is 0, so 3 and 564 are divisors of 1692)
...
1692 / 40 = 42.3 (the remainder is 12, so 40 is not a divisor of 1692)
1692 / 41 = 41.268292682927 (the remainder is 11, so 41 is not a divisor of 1692)