What are the divisors of 4299?

1, 3, 1433, 4299

There is a total of 4 positive divisors.
The sum of these divisors is 5736.
The arithmetic mean is 1434.

4 odd divisors

1, 3, 1433, 4299

How to compute the divisors of 4299?

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 4299 by each of the numbers from 1 to 4299 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)

4299 / 1 = 4299 (the remainder is 0, so 1 is a divisor of 4299)
4299 / 2 = 2149.5 (the remainder is 1, so 2 is not a divisor of 4299)
4299 / 3 = 1433 (the remainder is 0, so 3 is a divisor of 4299)
...
4299 / 4298 = 1.0002326663564 (the remainder is 1, so 4298 is not a divisor of 4299)
4299 / 4299 = 1 (the remainder is 0, so 4299 is a divisor of 4299)

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 4299 (i.e. 65.566759871142). 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 $\frac{N}{d} = D$ )

4299 / 1 = 4299 (the remainder is 0, so 1 and 4299 are divisors of 4299)
4299 / 2 = 2149.5 (the remainder is 1, so 2 is not a divisor of 4299)
4299 / 3 = 1433 (the remainder is 0, so 3 and 1433 are divisors of 4299)
...
4299 / 64 = 67.171875 (the remainder is 11, so 64 is not a divisor of 4299)
4299 / 65 = 66.138461538462 (the remainder is 9, so 65 is not a divisor of 4299)