What are the divisors of 5113?

1, 5113

There is a total of 2 positive divisors.
The sum of these divisors is 5114.
The arithmetic mean is 2557.

2 odd divisors

1, 5113

How to compute the divisors of 5113?

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 5113 by each of the numbers from 1 to 5113 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)

5113 / 1 = 5113 (the remainder is 0, so 1 is a divisor of 5113)
5113 / 2 = 2556.5 (the remainder is 1, so 2 is not a divisor of 5113)
5113 / 3 = 1704.3333333333 (the remainder is 1, so 3 is not a divisor of 5113)
...
5113 / 5112 = 1.0001956181534 (the remainder is 1, so 5112 is not a divisor of 5113)
5113 / 5113 = 1 (the remainder is 0, so 5113 is a divisor of 5113)

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 5113 (i.e. 71.505244562899). 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 $\frac{N}{d} = D$ )

5113 / 1 = 5113 (the remainder is 0, so 1 and 5113 are divisors of 5113)
5113 / 2 = 2556.5 (the remainder is 1, so 2 is not a divisor of 5113)
5113 / 3 = 1704.3333333333 (the remainder is 1, so 3 is not a divisor of 5113)
...
5113 / 70 = 73.042857142857 (the remainder is 3, so 70 is not a divisor of 5113)
5113 / 71 = 72.014084507042 (the remainder is 1, so 71 is not a divisor of 5113)