What are the divisors of 5880?

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 49, 56, 60, 70, 84, 98, 105, 120, 140, 147, 168, 196, 210, 245, 280, 294, 392, 420, 490, 588, 735, 840, 980, 1176, 1470, 1960, 2940, 5880

There is a total of 48 positive divisors.
The sum of these divisors is 20520.
The arithmetic mean is 427.5.

36 even divisors

2, 4, 6, 8, 10, 12, 14, 20, 24, 28, 30, 40, 42, 56, 60, 70, 84, 98, 120, 140, 168, 196, 210, 280, 294, 392, 420, 490, 588, 840, 980, 1176, 1470, 1960, 2940, 5880

12 odd divisors

1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735

How to compute the divisors of 5880?

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 5880 by each of the numbers from 1 to 5880 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)

5880 / 1 = 5880 (the remainder is 0, so 1 is a divisor of 5880)
5880 / 2 = 2940 (the remainder is 0, so 2 is a divisor of 5880)
5880 / 3 = 1960 (the remainder is 0, so 3 is a divisor of 5880)
...
5880 / 5879 = 1.0001700969553 (the remainder is 1, so 5879 is not a divisor of 5880)
5880 / 5880 = 1 (the remainder is 0, so 5880 is a divisor of 5880)

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 5880 (i.e. 76.681158050723). 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 $\frac{N}{d} = D$ )

5880 / 1 = 5880 (the remainder is 0, so 1 and 5880 are divisors of 5880)
5880 / 2 = 2940 (the remainder is 0, so 2 and 2940 are divisors of 5880)
5880 / 3 = 1960 (the remainder is 0, so 3 and 1960 are divisors of 5880)
...
5880 / 75 = 78.4 (the remainder is 30, so 75 is not a divisor of 5880)
5880 / 76 = 77.368421052632 (the remainder is 28, so 76 is not a divisor of 5880)