What are the divisors of 3241?

1, 7, 463, 3241

There is a total of 4 positive divisors.
The sum of these divisors is 3712.
The arithmetic mean is 928.

4 odd divisors

1, 7, 463, 3241

How to compute the divisors of 3241?

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 3241 by each of the numbers from 1 to 3241 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)

3241 / 1 = 3241 (the remainder is 0, so 1 is a divisor of 3241)
3241 / 2 = 1620.5 (the remainder is 1, so 2 is not a divisor of 3241)
3241 / 3 = 1080.3333333333 (the remainder is 1, so 3 is not a divisor of 3241)
...
3241 / 3240 = 1.0003086419753 (the remainder is 1, so 3240 is not a divisor of 3241)
3241 / 3241 = 1 (the remainder is 0, so 3241 is a divisor of 3241)

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 3241 (i.e. 56.929781309961). 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 $\frac{N}{d} = D$ )

3241 / 1 = 3241 (the remainder is 0, so 1 and 3241 are divisors of 3241)
3241 / 2 = 1620.5 (the remainder is 1, so 2 is not a divisor of 3241)
3241 / 3 = 1080.3333333333 (the remainder is 1, so 3 is not a divisor of 3241)
...
3241 / 55 = 58.927272727273 (the remainder is 51, so 55 is not a divisor of 3241)
3241 / 56 = 57.875 (the remainder is 49, so 56 is not a divisor of 3241)