What are the divisors of 5227?

1, 5227

There is a total of 2 positive divisors.
The sum of these divisors is 5228.
The arithmetic mean is 2614.

2 odd divisors

1, 5227

How to compute the divisors of 5227?

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 5227 by each of the numbers from 1 to 5227 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)

5227 / 1 = 5227 (the remainder is 0, so 1 is a divisor of 5227)
5227 / 2 = 2613.5 (the remainder is 1, so 2 is not a divisor of 5227)
5227 / 3 = 1742.3333333333 (the remainder is 1, so 3 is not a divisor of 5227)
...
5227 / 5226 = 1.0001913509376 (the remainder is 1, so 5226 is not a divisor of 5227)
5227 / 5227 = 1 (the remainder is 0, so 5227 is a divisor of 5227)

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 5227 (i.e. 72.29799443968). 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 $\frac{N}{d} = D$ )

5227 / 1 = 5227 (the remainder is 0, so 1 and 5227 are divisors of 5227)
5227 / 2 = 2613.5 (the remainder is 1, so 2 is not a divisor of 5227)
5227 / 3 = 1742.3333333333 (the remainder is 1, so 3 is not a divisor of 5227)
...
5227 / 71 = 73.619718309859 (the remainder is 44, so 71 is not a divisor of 5227)
5227 / 72 = 72.597222222222 (the remainder is 43, so 72 is not a divisor of 5227)