What are the divisors of 6022?

1, 2, 3011, 6022

There is a total of 4 positive divisors.
The sum of these divisors is 9036.
The arithmetic mean is 2259.

2 even divisors

2, 6022

2 odd divisors

1, 3011

How to compute the divisors of 6022?

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 6022 by each of the numbers from 1 to 6022 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)

6022 / 1 = 6022 (the remainder is 0, so 1 is a divisor of 6022)
6022 / 2 = 3011 (the remainder is 0, so 2 is a divisor of 6022)
6022 / 3 = 2007.3333333333 (the remainder is 1, so 3 is not a divisor of 6022)
...
6022 / 6021 = 1.0001660853679 (the remainder is 1, so 6021 is not a divisor of 6022)
6022 / 6022 = 1 (the remainder is 0, so 6022 is a divisor of 6022)

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 6022 (i.e. 77.601546376345). 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 $\frac{N}{d} = D$ )

6022 / 1 = 6022 (the remainder is 0, so 1 and 6022 are divisors of 6022)
6022 / 2 = 3011 (the remainder is 0, so 2 and 3011 are divisors of 6022)
6022 / 3 = 2007.3333333333 (the remainder is 1, so 3 is not a divisor of 6022)
...
6022 / 76 = 79.236842105263 (the remainder is 18, so 76 is not a divisor of 6022)
6022 / 77 = 78.207792207792 (the remainder is 16, so 77 is not a divisor of 6022)