What are the divisors of 283?

1, 283

There is a total of 2 positive divisors.
The sum of these divisors is 284.
The arithmetic mean is 142.

2 odd divisors

1, 283

How to compute the divisors of 283?

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 283 by each of the numbers from 1 to 283 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)

283 / 1 = 283 (the remainder is 0, so 1 is a divisor of 283)
283 / 2 = 141.5 (the remainder is 1, so 2 is not a divisor of 283)
283 / 3 = 94.333333333333 (the remainder is 1, so 3 is not a divisor of 283)
...
283 / 282 = 1.0035460992908 (the remainder is 1, so 282 is not a divisor of 283)
283 / 283 = 1 (the remainder is 0, so 283 is a divisor of 283)

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 283 (i.e. 16.822603841261). 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 $\frac{N}{d} = D$ )

283 / 1 = 283 (the remainder is 0, so 1 and 283 are divisors of 283)
283 / 2 = 141.5 (the remainder is 1, so 2 is not a divisor of 283)
283 / 3 = 94.333333333333 (the remainder is 1, so 3 is not a divisor of 283)
...
283 / 15 = 18.866666666667 (the remainder is 13, so 15 is not a divisor of 283)
283 / 16 = 17.6875 (the remainder is 11, so 16 is not a divisor of 283)