What are the divisors of 5311?

1, 47, 113, 5311

There is a total of 4 positive divisors.
The sum of these divisors is 5472.
The arithmetic mean is 1368.

4 odd divisors

1, 47, 113, 5311

How to compute the divisors of 5311?

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 5311 by each of the numbers from 1 to 5311 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)

5311 / 1 = 5311 (the remainder is 0, so 1 is a divisor of 5311)
5311 / 2 = 2655.5 (the remainder is 1, so 2 is not a divisor of 5311)
5311 / 3 = 1770.3333333333 (the remainder is 1, so 3 is not a divisor of 5311)
...
5311 / 5310 = 1.0001883239171 (the remainder is 1, so 5310 is not a divisor of 5311)
5311 / 5311 = 1 (the remainder is 0, so 5311 is a divisor of 5311)

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 5311 (i.e. 72.876608044008). 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 $\frac{N}{d} = D$ )

5311 / 1 = 5311 (the remainder is 0, so 1 and 5311 are divisors of 5311)
5311 / 2 = 2655.5 (the remainder is 1, so 2 is not a divisor of 5311)
5311 / 3 = 1770.3333333333 (the remainder is 1, so 3 is not a divisor of 5311)
...
5311 / 71 = 74.802816901408 (the remainder is 57, so 71 is not a divisor of 5311)
5311 / 72 = 73.763888888889 (the remainder is 55, so 72 is not a divisor of 5311)