What are the divisors of 3297?

1, 3, 7, 21, 157, 471, 1099, 3297

There is a total of 8 positive divisors.
The sum of these divisors is 5056.
The arithmetic mean is 632.

8 odd divisors

1, 3, 7, 21, 157, 471, 1099, 3297

How to compute the divisors of 3297?

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 3297 by each of the numbers from 1 to 3297 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)

3297 / 1 = 3297 (the remainder is 0, so 1 is a divisor of 3297)
3297 / 2 = 1648.5 (the remainder is 1, so 2 is not a divisor of 3297)
3297 / 3 = 1099 (the remainder is 0, so 3 is a divisor of 3297)
...
3297 / 3296 = 1.0003033980583 (the remainder is 1, so 3296 is not a divisor of 3297)
3297 / 3297 = 1 (the remainder is 0, so 3297 is a divisor of 3297)

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 3297 (i.e. 57.419508879822). 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 $\frac{N}{d} = D$ )

3297 / 1 = 3297 (the remainder is 0, so 1 and 3297 are divisors of 3297)
3297 / 2 = 1648.5 (the remainder is 1, so 2 is not a divisor of 3297)
3297 / 3 = 1099 (the remainder is 0, so 3 and 1099 are divisors of 3297)
...
3297 / 56 = 58.875 (the remainder is 49, so 56 is not a divisor of 3297)
3297 / 57 = 57.842105263158 (the remainder is 48, so 57 is not a divisor of 3297)