What are the divisors of 4227?

1, 3, 1409, 4227

There is a total of 4 positive divisors.
The sum of these divisors is 5640.
The arithmetic mean is 1410.

4 odd divisors

1, 3, 1409, 4227

How to compute the divisors of 4227?

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 4227 by each of the numbers from 1 to 4227 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)

4227 / 1 = 4227 (the remainder is 0, so 1 is a divisor of 4227)
4227 / 2 = 2113.5 (the remainder is 1, so 2 is not a divisor of 4227)
4227 / 3 = 1409 (the remainder is 0, so 3 is a divisor of 4227)
...
4227 / 4226 = 1.0002366303833 (the remainder is 1, so 4226 is not a divisor of 4227)
4227 / 4227 = 1 (the remainder is 0, so 4227 is a divisor of 4227)

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 4227 (i.e. 65.015382795151). 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 $\frac{N}{d} = D$ )

4227 / 1 = 4227 (the remainder is 0, so 1 and 4227 are divisors of 4227)
4227 / 2 = 2113.5 (the remainder is 1, so 2 is not a divisor of 4227)
4227 / 3 = 1409 (the remainder is 0, so 3 and 1409 are divisors of 4227)
...
4227 / 64 = 66.046875 (the remainder is 3, so 64 is not a divisor of 4227)
4227 / 65 = 65.030769230769 (the remainder is 2, so 65 is not a divisor of 4227)