What are the divisors of 1716?

1, 2, 3, 4, 6, 11, 12, 13, 22, 26, 33, 39, 44, 52, 66, 78, 132, 143, 156, 286, 429, 572, 858, 1716

There is a total of 24 positive divisors.
The sum of these divisors is 4704.
The arithmetic mean is 196.

16 even divisors

2, 4, 6, 12, 22, 26, 44, 52, 66, 78, 132, 156, 286, 572, 858, 1716

8 odd divisors

1, 3, 11, 13, 33, 39, 143, 429

How to compute the divisors of 1716?

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 1716 by each of the numbers from 1 to 1716 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)

1716 / 1 = 1716 (the remainder is 0, so 1 is a divisor of 1716)
1716 / 2 = 858 (the remainder is 0, so 2 is a divisor of 1716)
1716 / 3 = 572 (the remainder is 0, so 3 is a divisor of 1716)
...
1716 / 1715 = 1.000583090379 (the remainder is 1, so 1715 is not a divisor of 1716)
1716 / 1716 = 1 (the remainder is 0, so 1716 is a divisor of 1716)

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 1716 (i.e. 41.424630354416). 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 $\frac{N}{d} = D$ )

1716 / 1 = 1716 (the remainder is 0, so 1 and 1716 are divisors of 1716)
1716 / 2 = 858 (the remainder is 0, so 2 and 858 are divisors of 1716)
1716 / 3 = 572 (the remainder is 0, so 3 and 572 are divisors of 1716)
...
1716 / 40 = 42.9 (the remainder is 36, so 40 is not a divisor of 1716)
1716 / 41 = 41.853658536585 (the remainder is 35, so 41 is not a divisor of 1716)