What are the divisors of 2122?

1, 2, 1061, 2122

There is a total of 4 positive divisors.
The sum of these divisors is 3186.
The arithmetic mean is 796.5.

2 even divisors

2, 2122

2 odd divisors

1, 1061

How to compute the divisors of 2122?

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 2122 by each of the numbers from 1 to 2122 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)

2122 / 1 = 2122 (the remainder is 0, so 1 is a divisor of 2122)
2122 / 2 = 1061 (the remainder is 0, so 2 is a divisor of 2122)
2122 / 3 = 707.33333333333 (the remainder is 1, so 3 is not a divisor of 2122)
...
2122 / 2121 = 1.000471475719 (the remainder is 1, so 2121 is not a divisor of 2122)
2122 / 2122 = 1 (the remainder is 0, so 2122 is a divisor of 2122)

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 2122 (i.e. 46.065171225124). 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 $\frac{N}{d} = D$ )

2122 / 1 = 2122 (the remainder is 0, so 1 and 2122 are divisors of 2122)
2122 / 2 = 1061 (the remainder is 0, so 2 and 1061 are divisors of 2122)
2122 / 3 = 707.33333333333 (the remainder is 1, so 3 is not a divisor of 2122)
...
2122 / 45 = 47.155555555556 (the remainder is 7, so 45 is not a divisor of 2122)
2122 / 46 = 46.130434782609 (the remainder is 6, so 46 is not a divisor of 2122)