What are the divisors of 5702?

1, 2, 2851, 5702

There is a total of 4 positive divisors.
The sum of these divisors is 8556.
The arithmetic mean is 2139.

2 even divisors

2, 5702

2 odd divisors

1, 2851

How to compute the divisors of 5702?

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 5702 by each of the numbers from 1 to 5702 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)

5702 / 1 = 5702 (the remainder is 0, so 1 is a divisor of 5702)
5702 / 2 = 2851 (the remainder is 0, so 2 is a divisor of 5702)
5702 / 3 = 1900.6666666667 (the remainder is 2, so 3 is not a divisor of 5702)
...
5702 / 5701 = 1.0001754078232 (the remainder is 1, so 5701 is not a divisor of 5702)
5702 / 5702 = 1 (the remainder is 0, so 5702 is a divisor of 5702)

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 5702 (i.e. 75.511588514611). 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 $\frac{N}{d} = D$ )

5702 / 1 = 5702 (the remainder is 0, so 1 and 5702 are divisors of 5702)
5702 / 2 = 2851 (the remainder is 0, so 2 and 2851 are divisors of 5702)
5702 / 3 = 1900.6666666667 (the remainder is 2, so 3 is not a divisor of 5702)
...
5702 / 74 = 77.054054054054 (the remainder is 4, so 74 is not a divisor of 5702)
5702 / 75 = 76.026666666667 (the remainder is 2, so 75 is not a divisor of 5702)