What are the divisors of 286?

1, 2, 11, 13, 22, 26, 143, 286

There is a total of 8 positive divisors.
The sum of these divisors is 504.
The arithmetic mean is 63.

4 even divisors

2, 22, 26, 286

4 odd divisors

1, 11, 13, 143

How to compute the divisors of 286?

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 286 by each of the numbers from 1 to 286 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)

286 / 1 = 286 (the remainder is 0, so 1 is a divisor of 286)
286 / 2 = 143 (the remainder is 0, so 2 is a divisor of 286)
286 / 3 = 95.333333333333 (the remainder is 1, so 3 is not a divisor of 286)
...
286 / 285 = 1.0035087719298 (the remainder is 1, so 285 is not a divisor of 286)
286 / 286 = 1 (the remainder is 0, so 286 is a divisor of 286)

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 286 (i.e. 16.911534525288). 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 $\frac{N}{d} = D$ )

286 / 1 = 286 (the remainder is 0, so 1 and 286 are divisors of 286)
286 / 2 = 143 (the remainder is 0, so 2 and 143 are divisors of 286)
286 / 3 = 95.333333333333 (the remainder is 1, so 3 is not a divisor of 286)
...
286 / 15 = 19.066666666667 (the remainder is 1, so 15 is not a divisor of 286)
286 / 16 = 17.875 (the remainder is 14, so 16 is not a divisor of 286)