What are the divisors of 5565?

1, 3, 5, 7, 15, 21, 35, 53, 105, 159, 265, 371, 795, 1113, 1855, 5565

There is a total of 16 positive divisors.
The sum of these divisors is 10368.
The arithmetic mean is 648.

16 odd divisors

1, 3, 5, 7, 15, 21, 35, 53, 105, 159, 265, 371, 795, 1113, 1855, 5565

How to compute the divisors of 5565?

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 5565 by each of the numbers from 1 to 5565 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)

5565 / 1 = 5565 (the remainder is 0, so 1 is a divisor of 5565)
5565 / 2 = 2782.5 (the remainder is 1, so 2 is not a divisor of 5565)
5565 / 3 = 1855 (the remainder is 0, so 3 is a divisor of 5565)
...
5565 / 5564 = 1.0001797268152 (the remainder is 1, so 5564 is not a divisor of 5565)
5565 / 5565 = 1 (the remainder is 0, so 5565 is a divisor of 5565)

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 5565 (i.e. 74.598927606233). 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 $\frac{N}{d} = D$ )

5565 / 1 = 5565 (the remainder is 0, so 1 and 5565 are divisors of 5565)
5565 / 2 = 2782.5 (the remainder is 1, so 2 is not a divisor of 5565)
5565 / 3 = 1855 (the remainder is 0, so 3 and 1855 are divisors of 5565)
...
5565 / 73 = 76.232876712329 (the remainder is 17, so 73 is not a divisor of 5565)
5565 / 74 = 75.202702702703 (the remainder is 15, so 74 is not a divisor of 5565)