What are the divisors of 5261?

1, 5261

There is a total of 2 positive divisors.
The sum of these divisors is 5262.
The arithmetic mean is 2631.

2 odd divisors

1, 5261

How to compute the divisors of 5261?

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 5261 by each of the numbers from 1 to 5261 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)

5261 / 1 = 5261 (the remainder is 0, so 1 is a divisor of 5261)
5261 / 2 = 2630.5 (the remainder is 1, so 2 is not a divisor of 5261)
5261 / 3 = 1753.6666666667 (the remainder is 2, so 3 is not a divisor of 5261)
...
5261 / 5260 = 1.0001901140684 (the remainder is 1, so 5260 is not a divisor of 5261)
5261 / 5261 = 1 (the remainder is 0, so 5261 is a divisor of 5261)

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 5261 (i.e. 72.532751223154). 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 $\frac{N}{d} = D$ )

5261 / 1 = 5261 (the remainder is 0, so 1 and 5261 are divisors of 5261)
5261 / 2 = 2630.5 (the remainder is 1, so 2 is not a divisor of 5261)
5261 / 3 = 1753.6666666667 (the remainder is 2, so 3 is not a divisor of 5261)
...
5261 / 71 = 74.098591549296 (the remainder is 7, so 71 is not a divisor of 5261)
5261 / 72 = 73.069444444444 (the remainder is 5, so 72 is not a divisor of 5261)