What are the divisors of 3022?

1, 2, 1511, 3022

There is a total of 4 positive divisors.
The sum of these divisors is 4536.
The arithmetic mean is 1134.

2 even divisors

2, 3022

2 odd divisors

1, 1511

How to compute the divisors of 3022?

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 3022 by each of the numbers from 1 to 3022 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)

3022 / 1 = 3022 (the remainder is 0, so 1 is a divisor of 3022)
3022 / 2 = 1511 (the remainder is 0, so 2 is a divisor of 3022)
3022 / 3 = 1007.3333333333 (the remainder is 1, so 3 is not a divisor of 3022)
...
3022 / 3021 = 1.0003310162198 (the remainder is 1, so 3021 is not a divisor of 3022)
3022 / 3022 = 1 (the remainder is 0, so 3022 is a divisor of 3022)

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 3022 (i.e. 54.972720507539). 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 $\frac{N}{d} = D$ )

3022 / 1 = 3022 (the remainder is 0, so 1 and 3022 are divisors of 3022)
3022 / 2 = 1511 (the remainder is 0, so 2 and 1511 are divisors of 3022)
3022 / 3 = 1007.3333333333 (the remainder is 1, so 3 is not a divisor of 3022)
...
3022 / 53 = 57.018867924528 (the remainder is 1, so 53 is not a divisor of 3022)
3022 / 54 = 55.962962962963 (the remainder is 52, so 54 is not a divisor of 3022)