What are the divisors of 5894?

1, 2, 7, 14, 421, 842, 2947, 5894

There is a total of 8 positive divisors.
The sum of these divisors is 10128.
The arithmetic mean is 1266.

4 even divisors

2, 14, 842, 5894

4 odd divisors

1, 7, 421, 2947

How to compute the divisors of 5894?

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 5894 by each of the numbers from 1 to 5894 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)

5894 / 1 = 5894 (the remainder is 0, so 1 is a divisor of 5894)
5894 / 2 = 2947 (the remainder is 0, so 2 is a divisor of 5894)
5894 / 3 = 1964.6666666667 (the remainder is 2, so 3 is not a divisor of 5894)
...
5894 / 5893 = 1.0001696928559 (the remainder is 1, so 5893 is not a divisor of 5894)
5894 / 5894 = 1 (the remainder is 0, so 5894 is a divisor of 5894)

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 5894 (i.e. 76.772390870677). 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 $\frac{N}{d} = D$ )

5894 / 1 = 5894 (the remainder is 0, so 1 and 5894 are divisors of 5894)
5894 / 2 = 2947 (the remainder is 0, so 2 and 2947 are divisors of 5894)
5894 / 3 = 1964.6666666667 (the remainder is 2, so 3 is not a divisor of 5894)
...
5894 / 75 = 78.586666666667 (the remainder is 44, so 75 is not a divisor of 5894)
5894 / 76 = 77.552631578947 (the remainder is 42, so 76 is not a divisor of 5894)