What are the divisors of 5567?

1, 19, 293, 5567

There is a total of 4 positive divisors.
The sum of these divisors is 5880.
The arithmetic mean is 1470.

4 odd divisors

1, 19, 293, 5567

How to compute the divisors of 5567?

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 5567 by each of the numbers from 1 to 5567 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)

5567 / 1 = 5567 (the remainder is 0, so 1 is a divisor of 5567)
5567 / 2 = 2783.5 (the remainder is 1, so 2 is not a divisor of 5567)
5567 / 3 = 1855.6666666667 (the remainder is 2, so 3 is not a divisor of 5567)
...
5567 / 5566 = 1.000179662235 (the remainder is 1, so 5566 is not a divisor of 5567)
5567 / 5567 = 1 (the remainder is 0, so 5567 is a divisor of 5567)

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 5567 (i.e. 74.612331420483). 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 $\frac{N}{d} = D$ )

5567 / 1 = 5567 (the remainder is 0, so 1 and 5567 are divisors of 5567)
5567 / 2 = 2783.5 (the remainder is 1, so 2 is not a divisor of 5567)
5567 / 3 = 1855.6666666667 (the remainder is 2, so 3 is not a divisor of 5567)
...
5567 / 73 = 76.260273972603 (the remainder is 19, so 73 is not a divisor of 5567)
5567 / 74 = 75.22972972973 (the remainder is 17, so 74 is not a divisor of 5567)