What are the divisors of 3641?

1, 11, 331, 3641

There is a total of 4 positive divisors.
The sum of these divisors is 3984.
The arithmetic mean is 996.

4 odd divisors

1, 11, 331, 3641

How to compute the divisors of 3641?

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 3641 by each of the numbers from 1 to 3641 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)

3641 / 1 = 3641 (the remainder is 0, so 1 is a divisor of 3641)
3641 / 2 = 1820.5 (the remainder is 1, so 2 is not a divisor of 3641)
3641 / 3 = 1213.6666666667 (the remainder is 2, so 3 is not a divisor of 3641)
...
3641 / 3640 = 1.0002747252747 (the remainder is 1, so 3640 is not a divisor of 3641)
3641 / 3641 = 1 (the remainder is 0, so 3641 is a divisor of 3641)

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 3641 (i.e. 60.340699366182). 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 $\frac{N}{d} = D$ )

3641 / 1 = 3641 (the remainder is 0, so 1 and 3641 are divisors of 3641)
3641 / 2 = 1820.5 (the remainder is 1, so 2 is not a divisor of 3641)
3641 / 3 = 1213.6666666667 (the remainder is 2, so 3 is not a divisor of 3641)
...
3641 / 59 = 61.71186440678 (the remainder is 42, so 59 is not a divisor of 3641)
3641 / 60 = 60.683333333333 (the remainder is 41, so 60 is not a divisor of 3641)