What are the divisors of 4223?

1, 41, 103, 4223

There is a total of 4 positive divisors.
The sum of these divisors is 4368.
The arithmetic mean is 1092.

4 odd divisors

1, 41, 103, 4223

How to compute the divisors of 4223?

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 4223 by each of the numbers from 1 to 4223 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)

4223 / 1 = 4223 (the remainder is 0, so 1 is a divisor of 4223)
4223 / 2 = 2111.5 (the remainder is 1, so 2 is not a divisor of 4223)
4223 / 3 = 1407.6666666667 (the remainder is 2, so 3 is not a divisor of 4223)
...
4223 / 4222 = 1.0002368545713 (the remainder is 1, so 4222 is not a divisor of 4223)
4223 / 4223 = 1 (the remainder is 0, so 4223 is a divisor of 4223)

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 4223 (i.e. 64.98461356352). 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 $\frac{N}{d} = D$ )

4223 / 1 = 4223 (the remainder is 0, so 1 and 4223 are divisors of 4223)
4223 / 2 = 2111.5 (the remainder is 1, so 2 is not a divisor of 4223)
4223 / 3 = 1407.6666666667 (the remainder is 2, so 3 is not a divisor of 4223)
...
4223 / 63 = 67.031746031746 (the remainder is 2, so 63 is not a divisor of 4223)
4223 / 64 = 65.984375 (the remainder is 63, so 64 is not a divisor of 4223)