What are the divisors of 5178?

1, 2, 3, 6, 863, 1726, 2589, 5178

There is a total of 8 positive divisors.
The sum of these divisors is 10368.
The arithmetic mean is 1296.

4 even divisors

2, 6, 1726, 5178

4 odd divisors

1, 3, 863, 2589

How to compute the divisors of 5178?

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 5178 by each of the numbers from 1 to 5178 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)

5178 / 1 = 5178 (the remainder is 0, so 1 is a divisor of 5178)
5178 / 2 = 2589 (the remainder is 0, so 2 is a divisor of 5178)
5178 / 3 = 1726 (the remainder is 0, so 3 is a divisor of 5178)
...
5178 / 5177 = 1.000193162063 (the remainder is 1, so 5177 is not a divisor of 5178)
5178 / 5178 = 1 (the remainder is 0, so 5178 is a divisor of 5178)

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 5178 (i.e. 71.958321270024). 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 $\frac{N}{d} = D$ )

5178 / 1 = 5178 (the remainder is 0, so 1 and 5178 are divisors of 5178)
5178 / 2 = 2589 (the remainder is 0, so 2 and 2589 are divisors of 5178)
5178 / 3 = 1726 (the remainder is 0, so 3 and 1726 are divisors of 5178)
...
5178 / 70 = 73.971428571429 (the remainder is 68, so 70 is not a divisor of 5178)
5178 / 71 = 72.929577464789 (the remainder is 66, so 71 is not a divisor of 5178)