What are the divisors of 4287?

1, 3, 1429, 4287

There is a total of 4 positive divisors.
The sum of these divisors is 5720.
The arithmetic mean is 1430.

4 odd divisors

1, 3, 1429, 4287

How to compute the divisors of 4287?

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 4287 by each of the numbers from 1 to 4287 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)

4287 / 1 = 4287 (the remainder is 0, so 1 is a divisor of 4287)
4287 / 2 = 2143.5 (the remainder is 1, so 2 is not a divisor of 4287)
4287 / 3 = 1429 (the remainder is 0, so 3 is a divisor of 4287)
...
4287 / 4286 = 1.0002333177788 (the remainder is 1, so 4286 is not a divisor of 4287)
4287 / 4287 = 1 (the remainder is 0, so 4287 is a divisor of 4287)

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 4287 (i.e. 65.475186139483). 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 $\frac{N}{d} = D$ )

4287 / 1 = 4287 (the remainder is 0, so 1 and 4287 are divisors of 4287)
4287 / 2 = 2143.5 (the remainder is 1, so 2 is not a divisor of 4287)
4287 / 3 = 1429 (the remainder is 0, so 3 and 1429 are divisors of 4287)
...
4287 / 64 = 66.984375 (the remainder is 63, so 64 is not a divisor of 4287)
4287 / 65 = 65.953846153846 (the remainder is 62, so 65 is not a divisor of 4287)