What are the divisors of 5714?

1, 2, 2857, 5714

There is a total of 4 positive divisors.
The sum of these divisors is 8574.
The arithmetic mean is 2143.5.

2 even divisors

2, 5714

2 odd divisors

1, 2857

How to compute the divisors of 5714?

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 5714 by each of the numbers from 1 to 5714 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)

5714 / 1 = 5714 (the remainder is 0, so 1 is a divisor of 5714)
5714 / 2 = 2857 (the remainder is 0, so 2 is a divisor of 5714)
5714 / 3 = 1904.6666666667 (the remainder is 2, so 3 is not a divisor of 5714)
...
5714 / 5713 = 1.0001750393839 (the remainder is 1, so 5713 is not a divisor of 5714)
5714 / 5714 = 1 (the remainder is 0, so 5714 is a divisor of 5714)

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 5714 (i.e. 75.591004755857). 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 $\frac{N}{d} = D$ )

5714 / 1 = 5714 (the remainder is 0, so 1 and 5714 are divisors of 5714)
5714 / 2 = 2857 (the remainder is 0, so 2 and 2857 are divisors of 5714)
5714 / 3 = 1904.6666666667 (the remainder is 2, so 3 is not a divisor of 5714)
...
5714 / 74 = 77.216216216216 (the remainder is 16, so 74 is not a divisor of 5714)
5714 / 75 = 76.186666666667 (the remainder is 14, so 75 is not a divisor of 5714)