What are the divisors of 5164?

1, 2, 4, 1291, 2582, 5164

There is a total of 6 positive divisors.
The sum of these divisors is 9044.
The arithmetic mean is 1507.3333333333.

4 even divisors

2, 4, 2582, 5164

2 odd divisors

1, 1291

How to compute the divisors of 5164?

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 5164 by each of the numbers from 1 to 5164 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)

5164 / 1 = 5164 (the remainder is 0, so 1 is a divisor of 5164)
5164 / 2 = 2582 (the remainder is 0, so 2 is a divisor of 5164)
5164 / 3 = 1721.3333333333 (the remainder is 1, so 3 is not a divisor of 5164)
...
5164 / 5163 = 1.0001936858416 (the remainder is 1, so 5163 is not a divisor of 5164)
5164 / 5164 = 1 (the remainder is 0, so 5164 is a divisor of 5164)

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 5164 (i.e. 71.860976892887). 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 $\frac{N}{d} = D$ )

5164 / 1 = 5164 (the remainder is 0, so 1 and 5164 are divisors of 5164)
5164 / 2 = 2582 (the remainder is 0, so 2 and 2582 are divisors of 5164)
5164 / 3 = 1721.3333333333 (the remainder is 1, so 3 is not a divisor of 5164)
...
5164 / 70 = 73.771428571429 (the remainder is 54, so 70 is not a divisor of 5164)
5164 / 71 = 72.732394366197 (the remainder is 52, so 71 is not a divisor of 5164)