What are the divisors of 4680?

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 18, 20, 24, 26, 30, 36, 39, 40, 45, 52, 60, 65, 72, 78, 90, 104, 117, 120, 130, 156, 180, 195, 234, 260, 312, 360, 390, 468, 520, 585, 780, 936, 1170, 1560, 2340, 4680

There is a total of 48 positive divisors.
The sum of these divisors is 16380.
The arithmetic mean is 341.25.

36 even divisors

2, 4, 6, 8, 10, 12, 18, 20, 24, 26, 30, 36, 40, 52, 60, 72, 78, 90, 104, 120, 130, 156, 180, 234, 260, 312, 360, 390, 468, 520, 780, 936, 1170, 1560, 2340, 4680

12 odd divisors

1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585

How to compute the divisors of 4680?

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 4680 by each of the numbers from 1 to 4680 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)

4680 / 1 = 4680 (the remainder is 0, so 1 is a divisor of 4680)
4680 / 2 = 2340 (the remainder is 0, so 2 is a divisor of 4680)
4680 / 3 = 1560 (the remainder is 0, so 3 is a divisor of 4680)
...
4680 / 4679 = 1.0002137208805 (the remainder is 1, so 4679 is not a divisor of 4680)
4680 / 4680 = 1 (the remainder is 0, so 4680 is a divisor of 4680)

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 4680 (i.e. 68.410525505948). 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 $\frac{N}{d} = D$ )

4680 / 1 = 4680 (the remainder is 0, so 1 and 4680 are divisors of 4680)
4680 / 2 = 2340 (the remainder is 0, so 2 and 2340 are divisors of 4680)
4680 / 3 = 1560 (the remainder is 0, so 3 and 1560 are divisors of 4680)
...
4680 / 67 = 69.850746268657 (the remainder is 57, so 67 is not a divisor of 4680)
4680 / 68 = 68.823529411765 (the remainder is 56, so 68 is not a divisor of 4680)