What are the divisors of 4281?

1, 3, 1427, 4281

There is a total of 4 positive divisors.
The sum of these divisors is 5712.
The arithmetic mean is 1428.

4 odd divisors

1, 3, 1427, 4281

How to compute the divisors of 4281?

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 4281 by each of the numbers from 1 to 4281 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)

4281 / 1 = 4281 (the remainder is 0, so 1 is a divisor of 4281)
4281 / 2 = 2140.5 (the remainder is 1, so 2 is not a divisor of 4281)
4281 / 3 = 1427 (the remainder is 0, so 3 is a divisor of 4281)
...
4281 / 4280 = 1.0002336448598 (the remainder is 1, so 4280 is not a divisor of 4281)
4281 / 4281 = 1 (the remainder is 0, so 4281 is a divisor of 4281)

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 4281 (i.e. 65.429351211822). 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 $\frac{N}{d} = D$ )

4281 / 1 = 4281 (the remainder is 0, so 1 and 4281 are divisors of 4281)
4281 / 2 = 2140.5 (the remainder is 1, so 2 is not a divisor of 4281)
4281 / 3 = 1427 (the remainder is 0, so 3 and 1427 are divisors of 4281)
...
4281 / 64 = 66.890625 (the remainder is 57, so 64 is not a divisor of 4281)
4281 / 65 = 65.861538461538 (the remainder is 56, so 65 is not a divisor of 4281)