What are the divisors of 5569?

1, 5569

There is a total of 2 positive divisors.
The sum of these divisors is 5570.
The arithmetic mean is 2785.

2 odd divisors

1, 5569

How to compute the divisors of 5569?

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 5569 by each of the numbers from 1 to 5569 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)

5569 / 1 = 5569 (the remainder is 0, so 1 is a divisor of 5569)
5569 / 2 = 2784.5 (the remainder is 1, so 2 is not a divisor of 5569)
5569 / 3 = 1856.3333333333 (the remainder is 1, so 3 is not a divisor of 5569)
...
5569 / 5568 = 1.0001795977011 (the remainder is 1, so 5568 is not a divisor of 5569)
5569 / 5569 = 1 (the remainder is 0, so 5569 is a divisor of 5569)

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 5569 (i.e. 74.625732827223). 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 $\frac{N}{d} = D$ )

5569 / 1 = 5569 (the remainder is 0, so 1 and 5569 are divisors of 5569)
5569 / 2 = 2784.5 (the remainder is 1, so 2 is not a divisor of 5569)
5569 / 3 = 1856.3333333333 (the remainder is 1, so 3 is not a divisor of 5569)
...
5569 / 73 = 76.287671232877 (the remainder is 21, so 73 is not a divisor of 5569)
5569 / 74 = 75.256756756757 (the remainder is 19, so 74 is not a divisor of 5569)