What are the divisors of 4303?

1, 13, 331, 4303

There is a total of 4 positive divisors.
The sum of these divisors is 4648.
The arithmetic mean is 1162.

4 odd divisors

1, 13, 331, 4303

How to compute the divisors of 4303?

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 4303 by each of the numbers from 1 to 4303 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)

4303 / 1 = 4303 (the remainder is 0, so 1 is a divisor of 4303)
4303 / 2 = 2151.5 (the remainder is 1, so 2 is not a divisor of 4303)
4303 / 3 = 1434.3333333333 (the remainder is 1, so 3 is not a divisor of 4303)
...
4303 / 4302 = 1.0002324500232 (the remainder is 1, so 4302 is not a divisor of 4303)
4303 / 4303 = 1 (the remainder is 0, so 4303 is a divisor of 4303)

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 4303 (i.e. 65.597256040173). 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 $\frac{N}{d} = D$ )

4303 / 1 = 4303 (the remainder is 0, so 1 and 4303 are divisors of 4303)
4303 / 2 = 2151.5 (the remainder is 1, so 2 is not a divisor of 4303)
4303 / 3 = 1434.3333333333 (the remainder is 1, so 3 is not a divisor of 4303)
...
4303 / 64 = 67.234375 (the remainder is 15, so 64 is not a divisor of 4303)
4303 / 65 = 66.2 (the remainder is 13, so 65 is not a divisor of 4303)