What are the divisors of 4363?

1, 4363

There is a total of 2 positive divisors.
The sum of these divisors is 4364.
The arithmetic mean is 2182.

2 odd divisors

1, 4363

How to compute the divisors of 4363?

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 4363 by each of the numbers from 1 to 4363 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)

4363 / 1 = 4363 (the remainder is 0, so 1 is a divisor of 4363)
4363 / 2 = 2181.5 (the remainder is 1, so 2 is not a divisor of 4363)
4363 / 3 = 1454.3333333333 (the remainder is 1, so 3 is not a divisor of 4363)
...
4363 / 4362 = 1.0002292526364 (the remainder is 1, so 4362 is not a divisor of 4363)
4363 / 4363 = 1 (the remainder is 0, so 4363 is a divisor of 4363)

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 4363 (i.e. 66.053009015487). 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 $\frac{N}{d} = D$ )

4363 / 1 = 4363 (the remainder is 0, so 1 and 4363 are divisors of 4363)
4363 / 2 = 2181.5 (the remainder is 1, so 2 is not a divisor of 4363)
4363 / 3 = 1454.3333333333 (the remainder is 1, so 3 is not a divisor of 4363)
...
4363 / 65 = 67.123076923077 (the remainder is 8, so 65 is not a divisor of 4363)
4363 / 66 = 66.106060606061 (the remainder is 7, so 66 is not a divisor of 4363)