What are the divisors of 299?

1, 13, 23, 299

There is a total of 4 positive divisors.
The sum of these divisors is 336.
The arithmetic mean is 84.

4 odd divisors

1, 13, 23, 299

How to compute the divisors of 299?

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 299 by each of the numbers from 1 to 299 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)

299 / 1 = 299 (the remainder is 0, so 1 is a divisor of 299)
299 / 2 = 149.5 (the remainder is 1, so 2 is not a divisor of 299)
299 / 3 = 99.666666666667 (the remainder is 2, so 3 is not a divisor of 299)
...
299 / 298 = 1.003355704698 (the remainder is 1, so 298 is not a divisor of 299)
299 / 299 = 1 (the remainder is 0, so 299 is a divisor of 299)

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 299 (i.e. 17.291616465791). 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 $\frac{N}{d} = D$ )

299 / 1 = 299 (the remainder is 0, so 1 and 299 are divisors of 299)
299 / 2 = 149.5 (the remainder is 1, so 2 is not a divisor of 299)
299 / 3 = 99.666666666667 (the remainder is 2, so 3 is not a divisor of 299)
...
299 / 16 = 18.6875 (the remainder is 11, so 16 is not a divisor of 299)
299 / 17 = 17.588235294118 (the remainder is 10, so 17 is not a divisor of 299)