What are the divisors of 2242?

1, 2, 19, 38, 59, 118, 1121, 2242

There is a total of 8 positive divisors.
The sum of these divisors is 3600.
The arithmetic mean is 450.

4 even divisors

2, 38, 118, 2242

4 odd divisors

1, 19, 59, 1121

How to compute the divisors of 2242?

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 2242 by each of the numbers from 1 to 2242 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)

2242 / 1 = 2242 (the remainder is 0, so 1 is a divisor of 2242)
2242 / 2 = 1121 (the remainder is 0, so 2 is a divisor of 2242)
2242 / 3 = 747.33333333333 (the remainder is 1, so 3 is not a divisor of 2242)
...
2242 / 2241 = 1.0004462293619 (the remainder is 1, so 2241 is not a divisor of 2242)
2242 / 2242 = 1 (the remainder is 0, so 2242 is a divisor of 2242)

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 2242 (i.e. 47.349762407007). 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 $\frac{N}{d} = D$ )

2242 / 1 = 2242 (the remainder is 0, so 1 and 2242 are divisors of 2242)
2242 / 2 = 1121 (the remainder is 0, so 2 and 1121 are divisors of 2242)
2242 / 3 = 747.33333333333 (the remainder is 1, so 3 is not a divisor of 2242)
...
2242 / 46 = 48.739130434783 (the remainder is 34, so 46 is not a divisor of 2242)
2242 / 47 = 47.702127659574 (the remainder is 33, so 47 is not a divisor of 2242)