What are the divisors of 5475?

1, 3, 5, 15, 25, 73, 75, 219, 365, 1095, 1825, 5475

There is a total of 12 positive divisors.
The sum of these divisors is 9176.
The arithmetic mean is 764.66666666667.

12 odd divisors

1, 3, 5, 15, 25, 73, 75, 219, 365, 1095, 1825, 5475

How to compute the divisors of 5475?

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 5475 by each of the numbers from 1 to 5475 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)

5475 / 1 = 5475 (the remainder is 0, so 1 is a divisor of 5475)
5475 / 2 = 2737.5 (the remainder is 1, so 2 is not a divisor of 5475)
5475 / 3 = 1825 (the remainder is 0, so 3 is a divisor of 5475)
...
5475 / 5474 = 1.0001826817684 (the remainder is 1, so 5474 is not a divisor of 5475)
5475 / 5475 = 1 (the remainder is 0, so 5475 is a divisor of 5475)

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 5475 (i.e. 73.993242934744). 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 $\frac{N}{d} = D$ )

5475 / 1 = 5475 (the remainder is 0, so 1 and 5475 are divisors of 5475)
5475 / 2 = 2737.5 (the remainder is 1, so 2 is not a divisor of 5475)
5475 / 3 = 1825 (the remainder is 0, so 3 and 1825 are divisors of 5475)
...
5475 / 72 = 76.041666666667 (the remainder is 3, so 72 is not a divisor of 5475)
5475 / 73 = 75 (the remainder is 0, so 73 and 75 are divisors of 5475)