What are the divisors of 9240?

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 20, 21, 22, 24, 28, 30, 33, 35, 40, 42, 44, 55, 56, 60, 66, 70, 77, 84, 88, 105, 110, 120, 132, 140, 154, 165, 168, 210, 220, 231, 264, 280, 308, 330, 385, 420, 440, 462, 616, 660, 770, 840, 924, 1155, 1320, 1540, 1848, 2310, 3080, 4620, 9240

There is a total of 64 positive divisors.
The sum of these divisors is 34560.
The arithmetic mean is 540.

48 even divisors

2, 4, 6, 8, 10, 12, 14, 20, 22, 24, 28, 30, 40, 42, 44, 56, 60, 66, 70, 84, 88, 110, 120, 132, 140, 154, 168, 210, 220, 264, 280, 308, 330, 420, 440, 462, 616, 660, 770, 840, 924, 1320, 1540, 1848, 2310, 3080, 4620, 9240

16 odd divisors

1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385, 1155

How to compute the divisors of 9240?

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 9240 by each of the numbers from 1 to 9240 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)

9240 / 1 = 9240 (the remainder is 0, so 1 is a divisor of 9240)
9240 / 2 = 4620 (the remainder is 0, so 2 is a divisor of 9240)
9240 / 3 = 3080 (the remainder is 0, so 3 is a divisor of 9240)
...
9240 / 9239 = 1.0001082368222 (the remainder is 1, so 9239 is not a divisor of 9240)
9240 / 9240 = 1 (the remainder is 0, so 9240 is a divisor of 9240)

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 9240 (i.e. 96.124918725583). 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 $\frac{N}{d} = D$ )

9240 / 1 = 9240 (the remainder is 0, so 1 and 9240 are divisors of 9240)
9240 / 2 = 4620 (the remainder is 0, so 2 and 4620 are divisors of 9240)
9240 / 3 = 3080 (the remainder is 0, so 3 and 3080 are divisors of 9240)
...
9240 / 95 = 97.263157894737 (the remainder is 25, so 95 is not a divisor of 9240)
9240 / 96 = 96.25 (the remainder is 24, so 96 is not a divisor of 9240)