What are the divisors of 4374?

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458, 2187, 4374

There is a total of 16 positive divisors.
The sum of these divisors is 9840.
The arithmetic mean is 615.

8 even divisors

2, 6, 18, 54, 162, 486, 1458, 4374

8 odd divisors

1, 3, 9, 27, 81, 243, 729, 2187

How to compute the divisors of 4374?

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 4374 by each of the numbers from 1 to 4374 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)

4374 / 1 = 4374 (the remainder is 0, so 1 is a divisor of 4374)
4374 / 2 = 2187 (the remainder is 0, so 2 is a divisor of 4374)
4374 / 3 = 1458 (the remainder is 0, so 3 is a divisor of 4374)
...
4374 / 4373 = 1.0002286759662 (the remainder is 1, so 4373 is not a divisor of 4374)
4374 / 4374 = 1 (the remainder is 0, so 4374 is a divisor of 4374)

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 4374 (i.e. 66.136223055146). 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 $\frac{N}{d} = D$ )

4374 / 1 = 4374 (the remainder is 0, so 1 and 4374 are divisors of 4374)
4374 / 2 = 2187 (the remainder is 0, so 2 and 2187 are divisors of 4374)
4374 / 3 = 1458 (the remainder is 0, so 3 and 1458 are divisors of 4374)
...
4374 / 65 = 67.292307692308 (the remainder is 19, so 65 is not a divisor of 4374)
4374 / 66 = 66.272727272727 (the remainder is 18, so 66 is not a divisor of 4374)