What are the divisors of 293?

1, 293

There is a total of 2 positive divisors.
The sum of these divisors is 294.
The arithmetic mean is 147.

2 odd divisors

1, 293

How to compute the divisors of 293?

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 293 by each of the numbers from 1 to 293 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)

293 / 1 = 293 (the remainder is 0, so 1 is a divisor of 293)
293 / 2 = 146.5 (the remainder is 1, so 2 is not a divisor of 293)
293 / 3 = 97.666666666667 (the remainder is 2, so 3 is not a divisor of 293)
...
293 / 292 = 1.0034246575342 (the remainder is 1, so 292 is not a divisor of 293)
293 / 293 = 1 (the remainder is 0, so 293 is a divisor of 293)

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 293 (i.e. 17.117242768624). 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 $\frac{N}{d} = D$ )

293 / 1 = 293 (the remainder is 0, so 1 and 293 are divisors of 293)
293 / 2 = 146.5 (the remainder is 1, so 2 is not a divisor of 293)
293 / 3 = 97.666666666667 (the remainder is 2, so 3 is not a divisor of 293)
...
293 / 16 = 18.3125 (the remainder is 5, so 16 is not a divisor of 293)
293 / 17 = 17.235294117647 (the remainder is 4, so 17 is not a divisor of 293)