What are the divisors of 4422?

1, 2, 3, 6, 11, 22, 33, 66, 67, 134, 201, 402, 737, 1474, 2211, 4422

There is a total of 16 positive divisors.
The sum of these divisors is 9792.
The arithmetic mean is 612.

8 even divisors

2, 6, 22, 66, 134, 402, 1474, 4422

8 odd divisors

1, 3, 11, 33, 67, 201, 737, 2211

How to compute the divisors of 4422?

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 4422 by each of the numbers from 1 to 4422 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)

4422 / 1 = 4422 (the remainder is 0, so 1 is a divisor of 4422)
4422 / 2 = 2211 (the remainder is 0, so 2 is a divisor of 4422)
4422 / 3 = 1474 (the remainder is 0, so 3 is a divisor of 4422)
...
4422 / 4421 = 1.000226193169 (the remainder is 1, so 4421 is not a divisor of 4422)
4422 / 4422 = 1 (the remainder is 0, so 4422 is a divisor of 4422)

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 4422 (i.e. 66.498120274185). 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 $\frac{N}{d} = D$ )

4422 / 1 = 4422 (the remainder is 0, so 1 and 4422 are divisors of 4422)
4422 / 2 = 2211 (the remainder is 0, so 2 and 2211 are divisors of 4422)
4422 / 3 = 1474 (the remainder is 0, so 3 and 1474 are divisors of 4422)
...
4422 / 65 = 68.030769230769 (the remainder is 2, so 65 is not a divisor of 4422)
4422 / 66 = 67 (the remainder is 0, so 66 and 67 are divisors of 4422)