What are the divisors of 5694?

1, 2, 3, 6, 13, 26, 39, 73, 78, 146, 219, 438, 949, 1898, 2847, 5694

There is a total of 16 positive divisors.
The sum of these divisors is 12432.
The arithmetic mean is 777.

8 even divisors

2, 6, 26, 78, 146, 438, 1898, 5694

8 odd divisors

1, 3, 13, 39, 73, 219, 949, 2847

How to compute the divisors of 5694?

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 5694 by each of the numbers from 1 to 5694 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)

5694 / 1 = 5694 (the remainder is 0, so 1 is a divisor of 5694)
5694 / 2 = 2847 (the remainder is 0, so 2 is a divisor of 5694)
5694 / 3 = 1898 (the remainder is 0, so 3 is a divisor of 5694)
...
5694 / 5693 = 1.0001756543123 (the remainder is 1, so 5693 is not a divisor of 5694)
5694 / 5694 = 1 (the remainder is 0, so 5694 is a divisor of 5694)

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 5694 (i.e. 75.458597919654). 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 $\frac{N}{d} = D$ )

5694 / 1 = 5694 (the remainder is 0, so 1 and 5694 are divisors of 5694)
5694 / 2 = 2847 (the remainder is 0, so 2 and 2847 are divisors of 5694)
5694 / 3 = 1898 (the remainder is 0, so 3 and 1898 are divisors of 5694)
...
5694 / 74 = 76.945945945946 (the remainder is 70, so 74 is not a divisor of 5694)
5694 / 75 = 75.92 (the remainder is 69, so 75 is not a divisor of 5694)