What are the divisors of 5627?

1, 17, 331, 5627

There is a total of 4 positive divisors.
The sum of these divisors is 5976.
The arithmetic mean is 1494.

4 odd divisors

1, 17, 331, 5627

How to compute the divisors of 5627?

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 5627 by each of the numbers from 1 to 5627 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)

5627 / 1 = 5627 (the remainder is 0, so 1 is a divisor of 5627)
5627 / 2 = 2813.5 (the remainder is 1, so 2 is not a divisor of 5627)
5627 / 3 = 1875.6666666667 (the remainder is 2, so 3 is not a divisor of 5627)
...
5627 / 5626 = 1.0001777461785 (the remainder is 1, so 5626 is not a divisor of 5627)
5627 / 5627 = 1 (the remainder is 0, so 5627 is a divisor of 5627)

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 5627 (i.e. 75.013332148359). 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 $\frac{N}{d} = D$ )

5627 / 1 = 5627 (the remainder is 0, so 1 and 5627 are divisors of 5627)
5627 / 2 = 2813.5 (the remainder is 1, so 2 is not a divisor of 5627)
5627 / 3 = 1875.6666666667 (the remainder is 2, so 3 is not a divisor of 5627)
...
5627 / 74 = 76.040540540541 (the remainder is 3, so 74 is not a divisor of 5627)
5627 / 75 = 75.026666666667 (the remainder is 2, so 75 is not a divisor of 5627)