What are the divisors of 7022?

1, 2, 3511, 7022

There is a total of 4 positive divisors.
The sum of these divisors is 10536.
The arithmetic mean is 2634.

2 even divisors

2, 7022

2 odd divisors

1, 3511

How to compute the divisors of 7022?

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 7022 by each of the numbers from 1 to 7022 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)

7022 / 1 = 7022 (the remainder is 0, so 1 is a divisor of 7022)
7022 / 2 = 3511 (the remainder is 0, so 2 is a divisor of 7022)
7022 / 3 = 2340.6666666667 (the remainder is 2, so 3 is not a divisor of 7022)
...
7022 / 7021 = 1.0001424298533 (the remainder is 1, so 7021 is not a divisor of 7022)
7022 / 7022 = 1 (the remainder is 0, so 7022 is a divisor of 7022)

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 7022 (i.e. 83.797374660546). 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 $\frac{N}{d} = D$ )

7022 / 1 = 7022 (the remainder is 0, so 1 and 7022 are divisors of 7022)
7022 / 2 = 3511 (the remainder is 0, so 2 and 3511 are divisors of 7022)
7022 / 3 = 2340.6666666667 (the remainder is 2, so 3 is not a divisor of 7022)
...
7022 / 82 = 85.634146341463 (the remainder is 52, so 82 is not a divisor of 7022)
7022 / 83 = 84.602409638554 (the remainder is 50, so 83 is not a divisor of 7022)