What are the divisors of 5637?

1, 3, 1879, 5637

There is a total of 4 positive divisors.
The sum of these divisors is 7520.
The arithmetic mean is 1880.

4 odd divisors

1, 3, 1879, 5637

How to compute the divisors of 5637?

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 5637 by each of the numbers from 1 to 5637 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)

5637 / 1 = 5637 (the remainder is 0, so 1 is a divisor of 5637)
5637 / 2 = 2818.5 (the remainder is 1, so 2 is not a divisor of 5637)
5637 / 3 = 1879 (the remainder is 0, so 3 is a divisor of 5637)
...
5637 / 5636 = 1.000177430802 (the remainder is 1, so 5636 is not a divisor of 5637)
5637 / 5637 = 1 (the remainder is 0, so 5637 is a divisor of 5637)

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 5637 (i.e. 75.079957378784). 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 $\frac{N}{d} = D$ )

5637 / 1 = 5637 (the remainder is 0, so 1 and 5637 are divisors of 5637)
5637 / 2 = 2818.5 (the remainder is 1, so 2 is not a divisor of 5637)
5637 / 3 = 1879 (the remainder is 0, so 3 and 1879 are divisors of 5637)
...
5637 / 74 = 76.175675675676 (the remainder is 13, so 74 is not a divisor of 5637)
5637 / 75 = 75.16 (the remainder is 12, so 75 is not a divisor of 5637)