What are the divisors of 4434?

1, 2, 3, 6, 739, 1478, 2217, 4434

There is a total of 8 positive divisors.
The sum of these divisors is 8880.
The arithmetic mean is 1110.

4 even divisors

2, 6, 1478, 4434

4 odd divisors

1, 3, 739, 2217

How to compute the divisors of 4434?

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 4434 by each of the numbers from 1 to 4434 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)

4434 / 1 = 4434 (the remainder is 0, so 1 is a divisor of 4434)
4434 / 2 = 2217 (the remainder is 0, so 2 is a divisor of 4434)
4434 / 3 = 1478 (the remainder is 0, so 3 is a divisor of 4434)
...
4434 / 4433 = 1.0002255808707 (the remainder is 1, so 4433 is not a divisor of 4434)
4434 / 4434 = 1 (the remainder is 0, so 4434 is a divisor of 4434)

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 4434 (i.e. 66.588287258346). 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 $\frac{N}{d} = D$ )

4434 / 1 = 4434 (the remainder is 0, so 1 and 4434 are divisors of 4434)
4434 / 2 = 2217 (the remainder is 0, so 2 and 2217 are divisors of 4434)
4434 / 3 = 1478 (the remainder is 0, so 3 and 1478 are divisors of 4434)
...
4434 / 65 = 68.215384615385 (the remainder is 14, so 65 is not a divisor of 4434)
4434 / 66 = 67.181818181818 (the remainder is 12, so 66 is not a divisor of 4434)