What are the divisors of 5114?

1, 2, 2557, 5114

There is a total of 4 positive divisors.
The sum of these divisors is 7674.
The arithmetic mean is 1918.5.

2 even divisors

2, 5114

2 odd divisors

1, 2557

How to compute the divisors of 5114?

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 5114 by each of the numbers from 1 to 5114 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)

5114 / 1 = 5114 (the remainder is 0, so 1 is a divisor of 5114)
5114 / 2 = 2557 (the remainder is 0, so 2 is a divisor of 5114)
5114 / 3 = 1704.6666666667 (the remainder is 2, so 3 is not a divisor of 5114)
...
5114 / 5113 = 1.0001955798944 (the remainder is 1, so 5113 is not a divisor of 5114)
5114 / 5114 = 1 (the remainder is 0, so 5114 is a divisor of 5114)

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 5114 (i.e. 71.512236715125). 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 $\frac{N}{d} = D$ )

5114 / 1 = 5114 (the remainder is 0, so 1 and 5114 are divisors of 5114)
5114 / 2 = 2557 (the remainder is 0, so 2 and 2557 are divisors of 5114)
5114 / 3 = 1704.6666666667 (the remainder is 2, so 3 is not a divisor of 5114)
...
5114 / 70 = 73.057142857143 (the remainder is 4, so 70 is not a divisor of 5114)
5114 / 71 = 72.028169014085 (the remainder is 2, so 71 is not a divisor of 5114)