What are the divisors of 5279?

1, 5279

There is a total of 2 positive divisors.
The sum of these divisors is 5280.
The arithmetic mean is 2640.

2 odd divisors

1, 5279

How to compute the divisors of 5279?

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 5279 by each of the numbers from 1 to 5279 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)

5279 / 1 = 5279 (the remainder is 0, so 1 is a divisor of 5279)
5279 / 2 = 2639.5 (the remainder is 1, so 2 is not a divisor of 5279)
5279 / 3 = 1759.6666666667 (the remainder is 2, so 3 is not a divisor of 5279)
...
5279 / 5278 = 1.0001894657067 (the remainder is 1, so 5278 is not a divisor of 5279)
5279 / 5279 = 1 (the remainder is 0, so 5279 is a divisor of 5279)

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 5279 (i.e. 72.656727148971). 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 $\frac{N}{d} = D$ )

5279 / 1 = 5279 (the remainder is 0, so 1 and 5279 are divisors of 5279)
5279 / 2 = 2639.5 (the remainder is 1, so 2 is not a divisor of 5279)
5279 / 3 = 1759.6666666667 (the remainder is 2, so 3 is not a divisor of 5279)
...
5279 / 71 = 74.352112676056 (the remainder is 25, so 71 is not a divisor of 5279)
5279 / 72 = 73.319444444444 (the remainder is 23, so 72 is not a divisor of 5279)