What are the divisors of 4022?

1, 2, 2011, 4022

There is a total of 4 positive divisors.
The sum of these divisors is 6036.
The arithmetic mean is 1509.

2 even divisors

2, 4022

2 odd divisors

1, 2011

How to compute the divisors of 4022?

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 4022 by each of the numbers from 1 to 4022 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)

4022 / 1 = 4022 (the remainder is 0, so 1 is a divisor of 4022)
4022 / 2 = 2011 (the remainder is 0, so 2 is a divisor of 4022)
4022 / 3 = 1340.6666666667 (the remainder is 2, so 3 is not a divisor of 4022)
...
4022 / 4021 = 1.0002486943546 (the remainder is 1, so 4021 is not a divisor of 4022)
4022 / 4022 = 1 (the remainder is 0, so 4022 is a divisor of 4022)

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 4022 (i.e. 63.419239982832). 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 $\frac{N}{d} = D$ )

4022 / 1 = 4022 (the remainder is 0, so 1 and 4022 are divisors of 4022)
4022 / 2 = 2011 (the remainder is 0, so 2 and 2011 are divisors of 4022)
4022 / 3 = 1340.6666666667 (the remainder is 2, so 3 is not a divisor of 4022)
...
4022 / 62 = 64.870967741935 (the remainder is 54, so 62 is not a divisor of 4022)
4022 / 63 = 63.84126984127 (the remainder is 53, so 63 is not a divisor of 4022)