What are the divisors of 2422?

1, 2, 7, 14, 173, 346, 1211, 2422

There is a total of 8 positive divisors.
The sum of these divisors is 4176.
The arithmetic mean is 522.

4 even divisors

2, 14, 346, 2422

4 odd divisors

1, 7, 173, 1211

How to compute the divisors of 2422?

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 2422 by each of the numbers from 1 to 2422 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)

2422 / 1 = 2422 (the remainder is 0, so 1 is a divisor of 2422)
2422 / 2 = 1211 (the remainder is 0, so 2 is a divisor of 2422)
2422 / 3 = 807.33333333333 (the remainder is 1, so 3 is not a divisor of 2422)
...
2422 / 2421 = 1.0004130524577 (the remainder is 1, so 2421 is not a divisor of 2422)
2422 / 2422 = 1 (the remainder is 0, so 2422 is a divisor of 2422)

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 2422 (i.e. 49.213819197457). 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 $\frac{N}{d} = D$ )

2422 / 1 = 2422 (the remainder is 0, so 1 and 2422 are divisors of 2422)
2422 / 2 = 1211 (the remainder is 0, so 2 and 1211 are divisors of 2422)
2422 / 3 = 807.33333333333 (the remainder is 1, so 3 is not a divisor of 2422)
...
2422 / 48 = 50.458333333333 (the remainder is 22, so 48 is not a divisor of 2422)
2422 / 49 = 49.428571428571 (the remainder is 21, so 49 is not a divisor of 2422)