What are the divisors of 5595?

1, 3, 5, 15, 373, 1119, 1865, 5595

There is a total of 8 positive divisors.
The sum of these divisors is 8976.
The arithmetic mean is 1122.

8 odd divisors

1, 3, 5, 15, 373, 1119, 1865, 5595

How to compute the divisors of 5595?

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 5595 by each of the numbers from 1 to 5595 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)

5595 / 1 = 5595 (the remainder is 0, so 1 is a divisor of 5595)
5595 / 2 = 2797.5 (the remainder is 1, so 2 is not a divisor of 5595)
5595 / 3 = 1865 (the remainder is 0, so 3 is a divisor of 5595)
...
5595 / 5594 = 1.0001787629603 (the remainder is 1, so 5594 is not a divisor of 5595)
5595 / 5595 = 1 (the remainder is 0, so 5595 is a divisor of 5595)

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 5595 (i.e. 74.799732619843). 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 $\frac{N}{d} = D$ )

5595 / 1 = 5595 (the remainder is 0, so 1 and 5595 are divisors of 5595)
5595 / 2 = 2797.5 (the remainder is 1, so 2 is not a divisor of 5595)
5595 / 3 = 1865 (the remainder is 0, so 3 and 1865 are divisors of 5595)
...
5595 / 73 = 76.643835616438 (the remainder is 47, so 73 is not a divisor of 5595)
5595 / 74 = 75.608108108108 (the remainder is 45, so 74 is not a divisor of 5595)