What are the divisors of 4314?

1, 2, 3, 6, 719, 1438, 2157, 4314

There is a total of 8 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 1080.

4 even divisors

2, 6, 1438, 4314

4 odd divisors

1, 3, 719, 2157

How to compute the divisors of 4314?

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 4314 by each of the numbers from 1 to 4314 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)

4314 / 1 = 4314 (the remainder is 0, so 1 is a divisor of 4314)
4314 / 2 = 2157 (the remainder is 0, so 2 is a divisor of 4314)
4314 / 3 = 1438 (the remainder is 0, so 3 is a divisor of 4314)
...
4314 / 4313 = 1.000231857176 (the remainder is 1, so 4313 is not a divisor of 4314)
4314 / 4314 = 1 (the remainder is 0, so 4314 is a divisor of 4314)

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 4314 (i.e. 65.681047494692). 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 $\frac{N}{d} = D$ )

4314 / 1 = 4314 (the remainder is 0, so 1 and 4314 are divisors of 4314)
4314 / 2 = 2157 (the remainder is 0, so 2 and 2157 are divisors of 4314)
4314 / 3 = 1438 (the remainder is 0, so 3 and 1438 are divisors of 4314)
...
4314 / 64 = 67.40625 (the remainder is 26, so 64 is not a divisor of 4314)
4314 / 65 = 66.369230769231 (the remainder is 24, so 65 is not a divisor of 4314)