What are the divisors of 2222?

1, 2, 11, 22, 101, 202, 1111, 2222

There is a total of 8 positive divisors.
The sum of these divisors is 3672.
The arithmetic mean is 459.

4 even divisors

2, 22, 202, 2222

4 odd divisors

1, 11, 101, 1111

How to compute the divisors of 2222?

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 2222 by each of the numbers from 1 to 2222 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)

2222 / 1 = 2222 (the remainder is 0, so 1 is a divisor of 2222)
2222 / 2 = 1111 (the remainder is 0, so 2 is a divisor of 2222)
2222 / 3 = 740.66666666667 (the remainder is 2, so 3 is not a divisor of 2222)
...
2222 / 2221 = 1.0004502476362 (the remainder is 1, so 2221 is not a divisor of 2222)
2222 / 2222 = 1 (the remainder is 0, so 2222 is a divisor of 2222)

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 2222 (i.e. 47.138094997571). 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 $\frac{N}{d} = D$ )

2222 / 1 = 2222 (the remainder is 0, so 1 and 2222 are divisors of 2222)
2222 / 2 = 1111 (the remainder is 0, so 2 and 1111 are divisors of 2222)
2222 / 3 = 740.66666666667 (the remainder is 2, so 3 is not a divisor of 2222)
...
2222 / 46 = 48.304347826087 (the remainder is 14, so 46 is not a divisor of 2222)
2222 / 47 = 47.276595744681 (the remainder is 13, so 47 is not a divisor of 2222)