What are the divisors of 5265?

1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 81, 117, 135, 195, 351, 405, 585, 1053, 1755, 5265

There is a total of 20 positive divisors.
The sum of these divisors is 10164.
The arithmetic mean is 508.2.

20 odd divisors

1, 3, 5, 9, 13, 15, 27, 39, 45, 65, 81, 117, 135, 195, 351, 405, 585, 1053, 1755, 5265

How to compute the divisors of 5265?

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 5265 by each of the numbers from 1 to 5265 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)

5265 / 1 = 5265 (the remainder is 0, so 1 is a divisor of 5265)
5265 / 2 = 2632.5 (the remainder is 1, so 2 is not a divisor of 5265)
5265 / 3 = 1755 (the remainder is 0, so 3 is a divisor of 5265)
...
5265 / 5264 = 1.0001899696049 (the remainder is 1, so 5264 is not a divisor of 5265)
5265 / 5265 = 1 (the remainder is 0, so 5265 is a divisor of 5265)

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 5265 (i.e. 72.560319734687). 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 $\frac{N}{d} = D$ )

5265 / 1 = 5265 (the remainder is 0, so 1 and 5265 are divisors of 5265)
5265 / 2 = 2632.5 (the remainder is 1, so 2 is not a divisor of 5265)
5265 / 3 = 1755 (the remainder is 0, so 3 and 1755 are divisors of 5265)
...
5265 / 71 = 74.154929577465 (the remainder is 11, so 71 is not a divisor of 5265)
5265 / 72 = 73.125 (the remainder is 9, so 72 is not a divisor of 5265)