What are the divisors of 297?

1, 3, 9, 11, 27, 33, 99, 297

There is a total of 8 positive divisors.
The sum of these divisors is 480.
The arithmetic mean is 60.

8 odd divisors

1, 3, 9, 11, 27, 33, 99, 297

How to compute the divisors of 297?

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 297 by each of the numbers from 1 to 297 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)

297 / 1 = 297 (the remainder is 0, so 1 is a divisor of 297)
297 / 2 = 148.5 (the remainder is 1, so 2 is not a divisor of 297)
297 / 3 = 99 (the remainder is 0, so 3 is a divisor of 297)
...
297 / 296 = 1.0033783783784 (the remainder is 1, so 296 is not a divisor of 297)
297 / 297 = 1 (the remainder is 0, so 297 is a divisor of 297)

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 297 (i.e. 17.233687939614). 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 $\frac{N}{d} = D$ )

297 / 1 = 297 (the remainder is 0, so 1 and 297 are divisors of 297)
297 / 2 = 148.5 (the remainder is 1, so 2 is not a divisor of 297)
297 / 3 = 99 (the remainder is 0, so 3 and 99 are divisors of 297)
...
297 / 16 = 18.5625 (the remainder is 9, so 16 is not a divisor of 297)
297 / 17 = 17.470588235294 (the remainder is 8, so 17 is not a divisor of 297)