What are the divisors of 3249?

1, 3, 9, 19, 57, 171, 361, 1083, 3249

There is a total of 9 positive divisors.
The sum of these divisors is 4953.
The arithmetic mean is 550.33333333333.

9 odd divisors

1, 3, 9, 19, 57, 171, 361, 1083, 3249

How to compute the divisors of 3249?

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 3249 by each of the numbers from 1 to 3249 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)

3249 / 1 = 3249 (the remainder is 0, so 1 is a divisor of 3249)
3249 / 2 = 1624.5 (the remainder is 1, so 2 is not a divisor of 3249)
3249 / 3 = 1083 (the remainder is 0, so 3 is a divisor of 3249)
...
3249 / 3248 = 1.0003078817734 (the remainder is 1, so 3248 is not a divisor of 3249)
3249 / 3249 = 1 (the remainder is 0, so 3249 is a divisor of 3249)

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 3249 (i.e. 57). 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 $\frac{N}{d} = D$ )

3249 / 1 = 3249 (the remainder is 0, so 1 and 3249 are divisors of 3249)
3249 / 2 = 1624.5 (the remainder is 1, so 2 is not a divisor of 3249)
3249 / 3 = 1083 (the remainder is 0, so 3 and 1083 are divisors of 3249)
...
3249 / 56 = 58.017857142857 (the remainder is 1, so 56 is not a divisor of 3249)
3249 / 57 = 57 (the remainder is 0, so 57 and 57 are divisors of 3249)