What are the divisors of 7080?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 59, 60, 118, 120, 177, 236, 295, 354, 472, 590, 708, 885, 1180, 1416, 1770, 2360, 3540, 7080

There is a total of 32 positive divisors.
The sum of these divisors is 21600.
The arithmetic mean is 675.

24 even divisors

2, 4, 6, 8, 10, 12, 20, 24, 30, 40, 60, 118, 120, 236, 354, 472, 590, 708, 1180, 1416, 1770, 2360, 3540, 7080

8 odd divisors

1, 3, 5, 15, 59, 177, 295, 885

How to compute the divisors of 7080?

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 7080 by each of the numbers from 1 to 7080 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)

7080 / 1 = 7080 (the remainder is 0, so 1 is a divisor of 7080)
7080 / 2 = 3540 (the remainder is 0, so 2 is a divisor of 7080)
7080 / 3 = 2360 (the remainder is 0, so 3 is a divisor of 7080)
...
7080 / 7079 = 1.0001412628902 (the remainder is 1, so 7079 is not a divisor of 7080)
7080 / 7080 = 1 (the remainder is 0, so 7080 is a divisor of 7080)

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 7080 (i.e. 84.142735871851). 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 $\frac{N}{d} = D$ )

7080 / 1 = 7080 (the remainder is 0, so 1 and 7080 are divisors of 7080)
7080 / 2 = 3540 (the remainder is 0, so 2 and 3540 are divisors of 7080)
7080 / 3 = 2360 (the remainder is 0, so 3 and 2360 are divisors of 7080)
...
7080 / 83 = 85.301204819277 (the remainder is 25, so 83 is not a divisor of 7080)
7080 / 84 = 84.285714285714 (the remainder is 24, so 84 is not a divisor of 7080)