What are the divisors of 271?

1, 271

There is a total of 2 positive divisors.
The sum of these divisors is 272.
The arithmetic mean is 136.

2 odd divisors

1, 271

How to compute the divisors of 271?

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 271 by each of the numbers from 1 to 271 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)

271 / 1 = 271 (the remainder is 0, so 1 is a divisor of 271)
271 / 2 = 135.5 (the remainder is 1, so 2 is not a divisor of 271)
271 / 3 = 90.333333333333 (the remainder is 1, so 3 is not a divisor of 271)
...
271 / 270 = 1.0037037037037 (the remainder is 1, so 270 is not a divisor of 271)
271 / 271 = 1 (the remainder is 0, so 271 is a divisor of 271)

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 271 (i.e. 16.462077633154). 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 $\frac{N}{d} = D$ )

271 / 1 = 271 (the remainder is 0, so 1 and 271 are divisors of 271)
271 / 2 = 135.5 (the remainder is 1, so 2 is not a divisor of 271)
271 / 3 = 90.333333333333 (the remainder is 1, so 3 is not a divisor of 271)
...
271 / 15 = 18.066666666667 (the remainder is 1, so 15 is not a divisor of 271)
271 / 16 = 16.9375 (the remainder is 15, so 16 is not a divisor of 271)