What are the divisors of 3243?

1, 3, 23, 47, 69, 141, 1081, 3243

There is a total of 8 positive divisors.
The sum of these divisors is 4608.
The arithmetic mean is 576.

8 odd divisors

1, 3, 23, 47, 69, 141, 1081, 3243

How to compute the divisors of 3243?

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 3243 by each of the numbers from 1 to 3243 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)

3243 / 1 = 3243 (the remainder is 0, so 1 is a divisor of 3243)
3243 / 2 = 1621.5 (the remainder is 1, so 2 is not a divisor of 3243)
3243 / 3 = 1081 (the remainder is 0, so 3 is a divisor of 3243)
...
3243 / 3242 = 1.0003084515731 (the remainder is 1, so 3242 is not a divisor of 3243)
3243 / 3243 = 1 (the remainder is 0, so 3243 is a divisor of 3243)

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 3243 (i.e. 56.947344099615). 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 $\frac{N}{d} = D$ )

3243 / 1 = 3243 (the remainder is 0, so 1 and 3243 are divisors of 3243)
3243 / 2 = 1621.5 (the remainder is 1, so 2 is not a divisor of 3243)
3243 / 3 = 1081 (the remainder is 0, so 3 and 1081 are divisors of 3243)
...
3243 / 55 = 58.963636363636 (the remainder is 53, so 55 is not a divisor of 3243)
3243 / 56 = 57.910714285714 (the remainder is 51, so 56 is not a divisor of 3243)