What are the divisors of 3294?

1, 2, 3, 6, 9, 18, 27, 54, 61, 122, 183, 366, 549, 1098, 1647, 3294

There is a total of 16 positive divisors.
The sum of these divisors is 7440.
The arithmetic mean is 465.

8 even divisors

2, 6, 18, 54, 122, 366, 1098, 3294

8 odd divisors

1, 3, 9, 27, 61, 183, 549, 1647

How to compute the divisors of 3294?

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 3294 by each of the numbers from 1 to 3294 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)

3294 / 1 = 3294 (the remainder is 0, so 1 is a divisor of 3294)
3294 / 2 = 1647 (the remainder is 0, so 2 is a divisor of 3294)
3294 / 3 = 1098 (the remainder is 0, so 3 is a divisor of 3294)
...
3294 / 3293 = 1.000303674461 (the remainder is 1, so 3293 is not a divisor of 3294)
3294 / 3294 = 1 (the remainder is 0, so 3294 is a divisor of 3294)

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 3294 (i.e. 57.393379409127). 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 $\frac{N}{d} = D$ )

3294 / 1 = 3294 (the remainder is 0, so 1 and 3294 are divisors of 3294)
3294 / 2 = 1647 (the remainder is 0, so 2 and 1647 are divisors of 3294)
3294 / 3 = 1098 (the remainder is 0, so 3 and 1098 are divisors of 3294)
...
3294 / 56 = 58.821428571429 (the remainder is 46, so 56 is not a divisor of 3294)
3294 / 57 = 57.789473684211 (the remainder is 45, so 57 is not a divisor of 3294)