What are the divisors of 3631?

1, 3631

There is a total of 2 positive divisors.
The sum of these divisors is 3632.
The arithmetic mean is 1816.

2 odd divisors

1, 3631

How to compute the divisors of 3631?

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 3631 by each of the numbers from 1 to 3631 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)

3631 / 1 = 3631 (the remainder is 0, so 1 is a divisor of 3631)
3631 / 2 = 1815.5 (the remainder is 1, so 2 is not a divisor of 3631)
3631 / 3 = 1210.3333333333 (the remainder is 1, so 3 is not a divisor of 3631)
...
3631 / 3630 = 1.0002754820937 (the remainder is 1, so 3630 is not a divisor of 3631)
3631 / 3631 = 1 (the remainder is 0, so 3631 is a divisor of 3631)

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 3631 (i.e. 60.257779580731). 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 $\frac{N}{d} = D$ )

3631 / 1 = 3631 (the remainder is 0, so 1 and 3631 are divisors of 3631)
3631 / 2 = 1815.5 (the remainder is 1, so 2 is not a divisor of 3631)
3631 / 3 = 1210.3333333333 (the remainder is 1, so 3 is not a divisor of 3631)
...
3631 / 59 = 61.542372881356 (the remainder is 32, so 59 is not a divisor of 3631)
3631 / 60 = 60.516666666667 (the remainder is 31, so 60 is not a divisor of 3631)