What are the divisors of 307?

1, 307

There is a total of 2 positive divisors.
The sum of these divisors is 308.
The arithmetic mean is 154.

2 odd divisors

1, 307

How to compute the divisors of 307?

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 307 by each of the numbers from 1 to 307 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)

307 / 1 = 307 (the remainder is 0, so 1 is a divisor of 307)
307 / 2 = 153.5 (the remainder is 1, so 2 is not a divisor of 307)
307 / 3 = 102.33333333333 (the remainder is 1, so 3 is not a divisor of 307)
...
307 / 306 = 1.0032679738562 (the remainder is 1, so 306 is not a divisor of 307)
307 / 307 = 1 (the remainder is 0, so 307 is a divisor of 307)

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 307 (i.e. 17.521415467935). 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 $\frac{N}{d} = D$ )

307 / 1 = 307 (the remainder is 0, so 1 and 307 are divisors of 307)
307 / 2 = 153.5 (the remainder is 1, so 2 is not a divisor of 307)
307 / 3 = 102.33333333333 (the remainder is 1, so 3 is not a divisor of 307)
...
307 / 16 = 19.1875 (the remainder is 3, so 16 is not a divisor of 307)
307 / 17 = 18.058823529412 (the remainder is 1, so 17 is not a divisor of 307)