What are the divisors of 4286?

1, 2, 2143, 4286

There is a total of 4 positive divisors.
The sum of these divisors is 6432.
The arithmetic mean is 1608.

2 even divisors

2, 4286

2 odd divisors

1, 2143

How to compute the divisors of 4286?

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 4286 by each of the numbers from 1 to 4286 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)

4286 / 1 = 4286 (the remainder is 0, so 1 is a divisor of 4286)
4286 / 2 = 2143 (the remainder is 0, so 2 is a divisor of 4286)
4286 / 3 = 1428.6666666667 (the remainder is 2, so 3 is not a divisor of 4286)
...
4286 / 4285 = 1.0002333722287 (the remainder is 1, so 4285 is not a divisor of 4286)
4286 / 4286 = 1 (the remainder is 0, so 4286 is a divisor of 4286)

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 4286 (i.e. 65.467549213332). 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 $\frac{N}{d} = D$ )

4286 / 1 = 4286 (the remainder is 0, so 1 and 4286 are divisors of 4286)
4286 / 2 = 2143 (the remainder is 0, so 2 and 2143 are divisors of 4286)
4286 / 3 = 1428.6666666667 (the remainder is 2, so 3 is not a divisor of 4286)
...
4286 / 64 = 66.96875 (the remainder is 62, so 64 is not a divisor of 4286)
4286 / 65 = 65.938461538462 (the remainder is 61, so 65 is not a divisor of 4286)