What are the divisors of 1122?

1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122

There is a total of 16 positive divisors.
The sum of these divisors is 2592.
The arithmetic mean is 162.

8 even divisors

2, 6, 22, 34, 66, 102, 374, 1122

8 odd divisors

1, 3, 11, 17, 33, 51, 187, 561

How to compute the divisors of 1122?

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 1122 by each of the numbers from 1 to 1122 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)

1122 / 1 = 1122 (the remainder is 0, so 1 is a divisor of 1122)
1122 / 2 = 561 (the remainder is 0, so 2 is a divisor of 1122)
1122 / 3 = 374 (the remainder is 0, so 3 is a divisor of 1122)
...
1122 / 1121 = 1.0008920606601 (the remainder is 1, so 1121 is not a divisor of 1122)
1122 / 1122 = 1 (the remainder is 0, so 1122 is a divisor of 1122)

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 1122 (i.e. 33.496268448888). 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 $\frac{N}{d} = D$ )

1122 / 1 = 1122 (the remainder is 0, so 1 and 1122 are divisors of 1122)
1122 / 2 = 561 (the remainder is 0, so 2 and 561 are divisors of 1122)
1122 / 3 = 374 (the remainder is 0, so 3 and 374 are divisors of 1122)
...
1122 / 32 = 35.0625 (the remainder is 2, so 32 is not a divisor of 1122)
1122 / 33 = 34 (the remainder is 0, so 33 and 34 are divisors of 1122)