What are the divisors of 4426?

1, 2, 2213, 4426

There is a total of 4 positive divisors.
The sum of these divisors is 6642.
The arithmetic mean is 1660.5.

2 even divisors

2, 4426

2 odd divisors

1, 2213

How to compute the divisors of 4426?

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 4426 by each of the numbers from 1 to 4426 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)

4426 / 1 = 4426 (the remainder is 0, so 1 is a divisor of 4426)
4426 / 2 = 2213 (the remainder is 0, so 2 is a divisor of 4426)
4426 / 3 = 1475.3333333333 (the remainder is 1, so 3 is not a divisor of 4426)
...
4426 / 4425 = 1.0002259887006 (the remainder is 1, so 4425 is not a divisor of 4426)
4426 / 4426 = 1 (the remainder is 0, so 4426 is a divisor of 4426)

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 4426 (i.e. 66.52818951392). 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 $\frac{N}{d} = D$ )

4426 / 1 = 4426 (the remainder is 0, so 1 and 4426 are divisors of 4426)
4426 / 2 = 2213 (the remainder is 0, so 2 and 2213 are divisors of 4426)
4426 / 3 = 1475.3333333333 (the remainder is 1, so 3 is not a divisor of 4426)
...
4426 / 65 = 68.092307692308 (the remainder is 6, so 65 is not a divisor of 4426)
4426 / 66 = 67.060606060606 (the remainder is 4, so 66 is not a divisor of 4426)