What are the divisors of 4716?

1, 2, 3, 4, 6, 9, 12, 18, 36, 131, 262, 393, 524, 786, 1179, 1572, 2358, 4716

There is a total of 18 positive divisors.
The sum of these divisors is 12012.
The arithmetic mean is 667.33333333333.

12 even divisors

2, 4, 6, 12, 18, 36, 262, 524, 786, 1572, 2358, 4716

6 odd divisors

1, 3, 9, 131, 393, 1179

How to compute the divisors of 4716?

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 4716 by each of the numbers from 1 to 4716 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)

4716 / 1 = 4716 (the remainder is 0, so 1 is a divisor of 4716)
4716 / 2 = 2358 (the remainder is 0, so 2 is a divisor of 4716)
4716 / 3 = 1572 (the remainder is 0, so 3 is a divisor of 4716)
...
4716 / 4715 = 1.0002120890774 (the remainder is 1, so 4715 is not a divisor of 4716)
4716 / 4716 = 1 (the remainder is 0, so 4716 is a divisor of 4716)

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 4716 (i.e. 68.673138853558). 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 $\frac{N}{d} = D$ )

4716 / 1 = 4716 (the remainder is 0, so 1 and 4716 are divisors of 4716)
4716 / 2 = 2358 (the remainder is 0, so 2 and 2358 are divisors of 4716)
4716 / 3 = 1572 (the remainder is 0, so 3 and 1572 are divisors of 4716)
...
4716 / 67 = 70.388059701493 (the remainder is 26, so 67 is not a divisor of 4716)
4716 / 68 = 69.352941176471 (the remainder is 24, so 68 is not a divisor of 4716)