What are the divisors of 4338?

1, 2, 3, 6, 9, 18, 241, 482, 723, 1446, 2169, 4338

There is a total of 12 positive divisors.
The sum of these divisors is 9438.
The arithmetic mean is 786.5.

6 even divisors

2, 6, 18, 482, 1446, 4338

6 odd divisors

1, 3, 9, 241, 723, 2169

How to compute the divisors of 4338?

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 4338 by each of the numbers from 1 to 4338 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)

4338 / 1 = 4338 (the remainder is 0, so 1 is a divisor of 4338)
4338 / 2 = 2169 (the remainder is 0, so 2 is a divisor of 4338)
4338 / 3 = 1446 (the remainder is 0, so 3 is a divisor of 4338)
...
4338 / 4337 = 1.0002305741296 (the remainder is 1, so 4337 is not a divisor of 4338)
4338 / 4338 = 1 (the remainder is 0, so 4338 is a divisor of 4338)

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 4338 (i.e. 65.8634952003). 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 $\frac{N}{d} = D$ )

4338 / 1 = 4338 (the remainder is 0, so 1 and 4338 are divisors of 4338)
4338 / 2 = 2169 (the remainder is 0, so 2 and 2169 are divisors of 4338)
4338 / 3 = 1446 (the remainder is 0, so 3 and 1446 are divisors of 4338)
...
4338 / 64 = 67.78125 (the remainder is 50, so 64 is not a divisor of 4338)
4338 / 65 = 66.738461538462 (the remainder is 48, so 65 is not a divisor of 4338)