What are the divisors of 5142?

1, 2, 3, 6, 857, 1714, 2571, 5142

There is a total of 8 positive divisors.
The sum of these divisors is 10296.
The arithmetic mean is 1287.

4 even divisors

2, 6, 1714, 5142

4 odd divisors

1, 3, 857, 2571

How to compute the divisors of 5142?

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 5142 by each of the numbers from 1 to 5142 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)

5142 / 1 = 5142 (the remainder is 0, so 1 is a divisor of 5142)
5142 / 2 = 2571 (the remainder is 0, so 2 is a divisor of 5142)
5142 / 3 = 1714 (the remainder is 0, so 3 is a divisor of 5142)
...
5142 / 5141 = 1.0001945146859 (the remainder is 1, so 5141 is not a divisor of 5142)
5142 / 5142 = 1 (the remainder is 0, so 5142 is a divisor of 5142)

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 5142 (i.e. 71.70774016799). 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 $\frac{N}{d} = D$ )

5142 / 1 = 5142 (the remainder is 0, so 1 and 5142 are divisors of 5142)
5142 / 2 = 2571 (the remainder is 0, so 2 and 2571 are divisors of 5142)
5142 / 3 = 1714 (the remainder is 0, so 3 and 1714 are divisors of 5142)
...
5142 / 70 = 73.457142857143 (the remainder is 32, so 70 is not a divisor of 5142)
5142 / 71 = 72.422535211268 (the remainder is 30, so 71 is not a divisor of 5142)