What are the divisors of 5281?

1, 5281

There is a total of 2 positive divisors.
The sum of these divisors is 5282.
The arithmetic mean is 2641.

2 odd divisors

1, 5281

How to compute the divisors of 5281?

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 5281 by each of the numbers from 1 to 5281 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)

5281 / 1 = 5281 (the remainder is 0, so 1 is a divisor of 5281)
5281 / 2 = 2640.5 (the remainder is 1, so 2 is not a divisor of 5281)
5281 / 3 = 1760.3333333333 (the remainder is 1, so 3 is not a divisor of 5281)
...
5281 / 5280 = 1.0001893939394 (the remainder is 1, so 5280 is not a divisor of 5281)
5281 / 5281 = 1 (the remainder is 0, so 5281 is a divisor of 5281)

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 5281 (i.e. 72.670489196097). 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 $\frac{N}{d} = D$ )

5281 / 1 = 5281 (the remainder is 0, so 1 and 5281 are divisors of 5281)
5281 / 2 = 2640.5 (the remainder is 1, so 2 is not a divisor of 5281)
5281 / 3 = 1760.3333333333 (the remainder is 1, so 3 is not a divisor of 5281)
...
5281 / 71 = 74.380281690141 (the remainder is 27, so 71 is not a divisor of 5281)
5281 / 72 = 73.347222222222 (the remainder is 25, so 72 is not a divisor of 5281)