What are the divisors of 3299?

1, 3299

There is a total of 2 positive divisors.
The sum of these divisors is 3300.
The arithmetic mean is 1650.

2 odd divisors

1, 3299

How to compute the divisors of 3299?

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 3299 by each of the numbers from 1 to 3299 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)

3299 / 1 = 3299 (the remainder is 0, so 1 is a divisor of 3299)
3299 / 2 = 1649.5 (the remainder is 1, so 2 is not a divisor of 3299)
3299 / 3 = 1099.6666666667 (the remainder is 2, so 3 is not a divisor of 3299)
...
3299 / 3298 = 1.0003032140691 (the remainder is 1, so 3298 is not a divisor of 3299)
3299 / 3299 = 1 (the remainder is 0, so 3299 is a divisor of 3299)

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 3299 (i.e. 57.436921923098). 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 $\frac{N}{d} = D$ )

3299 / 1 = 3299 (the remainder is 0, so 1 and 3299 are divisors of 3299)
3299 / 2 = 1649.5 (the remainder is 1, so 2 is not a divisor of 3299)
3299 / 3 = 1099.6666666667 (the remainder is 2, so 3 is not a divisor of 3299)
...
3299 / 56 = 58.910714285714 (the remainder is 51, so 56 is not a divisor of 3299)
3299 / 57 = 57.877192982456 (the remainder is 50, so 57 is not a divisor of 3299)