What are the divisors of 281?

1, 281

There is a total of 2 positive divisors.
The sum of these divisors is 282.
The arithmetic mean is 141.

2 odd divisors

1, 281

How to compute the divisors of 281?

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 281 by each of the numbers from 1 to 281 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)

281 / 1 = 281 (the remainder is 0, so 1 is a divisor of 281)
281 / 2 = 140.5 (the remainder is 1, so 2 is not a divisor of 281)
281 / 3 = 93.666666666667 (the remainder is 2, so 3 is not a divisor of 281)
...
281 / 280 = 1.0035714285714 (the remainder is 1, so 280 is not a divisor of 281)
281 / 281 = 1 (the remainder is 0, so 281 is a divisor of 281)

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 281 (i.e. 16.76305461424). 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 $\frac{N}{d} = D$ )

281 / 1 = 281 (the remainder is 0, so 1 and 281 are divisors of 281)
281 / 2 = 140.5 (the remainder is 1, so 2 is not a divisor of 281)
281 / 3 = 93.666666666667 (the remainder is 2, so 3 is not a divisor of 281)
...
281 / 15 = 18.733333333333 (the remainder is 11, so 15 is not a divisor of 281)
281 / 16 = 17.5625 (the remainder is 9, so 16 is not a divisor of 281)