What are the divisors of 4442?

1, 2, 2221, 4442

There is a total of 4 positive divisors.
The sum of these divisors is 6666.
The arithmetic mean is 1666.5.

2 even divisors

2, 4442

2 odd divisors

1, 2221

How to compute the divisors of 4442?

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 4442 by each of the numbers from 1 to 4442 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)

4442 / 1 = 4442 (the remainder is 0, so 1 is a divisor of 4442)
4442 / 2 = 2221 (the remainder is 0, so 2 is a divisor of 4442)
4442 / 3 = 1480.6666666667 (the remainder is 2, so 3 is not a divisor of 4442)
...
4442 / 4441 = 1.0002251745102 (the remainder is 1, so 4441 is not a divisor of 4442)
4442 / 4442 = 1 (the remainder is 0, so 4442 is a divisor of 4442)

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 4442 (i.e. 66.648330811807). 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 $\frac{N}{d} = D$ )

4442 / 1 = 4442 (the remainder is 0, so 1 and 4442 are divisors of 4442)
4442 / 2 = 2221 (the remainder is 0, so 2 and 2221 are divisors of 4442)
4442 / 3 = 1480.6666666667 (the remainder is 2, so 3 is not a divisor of 4442)
...
4442 / 65 = 68.338461538462 (the remainder is 22, so 65 is not a divisor of 4442)
4442 / 66 = 67.30303030303 (the remainder is 20, so 66 is not a divisor of 4442)