What are the divisors of 4423?

1, 4423

There is a total of 2 positive divisors.
The sum of these divisors is 4424.
The arithmetic mean is 2212.

2 odd divisors

1, 4423

How to compute the divisors of 4423?

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 4423 by each of the numbers from 1 to 4423 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)

4423 / 1 = 4423 (the remainder is 0, so 1 is a divisor of 4423)
4423 / 2 = 2211.5 (the remainder is 1, so 2 is not a divisor of 4423)
4423 / 3 = 1474.3333333333 (the remainder is 1, so 3 is not a divisor of 4423)
...
4423 / 4422 = 1.0002261420172 (the remainder is 1, so 4422 is not a divisor of 4423)
4423 / 4423 = 1 (the remainder is 0, so 4423 is a divisor of 4423)

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 4423 (i.e. 66.505638858671). 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 $\frac{N}{d} = D$ )

4423 / 1 = 4423 (the remainder is 0, so 1 and 4423 are divisors of 4423)
4423 / 2 = 2211.5 (the remainder is 1, so 2 is not a divisor of 4423)
4423 / 3 = 1474.3333333333 (the remainder is 1, so 3 is not a divisor of 4423)
...
4423 / 65 = 68.046153846154 (the remainder is 3, so 65 is not a divisor of 4423)
4423 / 66 = 67.015151515152 (the remainder is 1, so 66 is not a divisor of 4423)