What are the divisors of 4333?

1, 7, 619, 4333

There is a total of 4 positive divisors.
The sum of these divisors is 4960.
The arithmetic mean is 1240.

4 odd divisors

1, 7, 619, 4333

How to compute the divisors of 4333?

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 4333 by each of the numbers from 1 to 4333 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)

4333 / 1 = 4333 (the remainder is 0, so 1 is a divisor of 4333)
4333 / 2 = 2166.5 (the remainder is 1, so 2 is not a divisor of 4333)
4333 / 3 = 1444.3333333333 (the remainder is 1, so 3 is not a divisor of 4333)
...
4333 / 4332 = 1.0002308402585 (the remainder is 1, so 4332 is not a divisor of 4333)
4333 / 4333 = 1 (the remainder is 0, so 4333 is a divisor of 4333)

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 4333 (i.e. 65.825526963329). 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 $\frac{N}{d} = D$ )

4333 / 1 = 4333 (the remainder is 0, so 1 and 4333 are divisors of 4333)
4333 / 2 = 2166.5 (the remainder is 1, so 2 is not a divisor of 4333)
4333 / 3 = 1444.3333333333 (the remainder is 1, so 3 is not a divisor of 4333)
...
4333 / 64 = 67.703125 (the remainder is 45, so 64 is not a divisor of 4333)
4333 / 65 = 66.661538461538 (the remainder is 43, so 65 is not a divisor of 4333)