What are the divisors of 3635?

1, 5, 727, 3635

There is a total of 4 positive divisors.
The sum of these divisors is 4368.
The arithmetic mean is 1092.

4 odd divisors

1, 5, 727, 3635

How to compute the divisors of 3635?

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 3635 by each of the numbers from 1 to 3635 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)

3635 / 1 = 3635 (the remainder is 0, so 1 is a divisor of 3635)
3635 / 2 = 1817.5 (the remainder is 1, so 2 is not a divisor of 3635)
3635 / 3 = 1211.6666666667 (the remainder is 2, so 3 is not a divisor of 3635)
...
3635 / 3634 = 1.0002751788663 (the remainder is 1, so 3634 is not a divisor of 3635)
3635 / 3635 = 1 (the remainder is 0, so 3635 is a divisor of 3635)

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 3635 (i.e. 60.290961179931). 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 $\frac{N}{d} = D$ )

3635 / 1 = 3635 (the remainder is 0, so 1 and 3635 are divisors of 3635)
3635 / 2 = 1817.5 (the remainder is 1, so 2 is not a divisor of 3635)
3635 / 3 = 1211.6666666667 (the remainder is 2, so 3 is not a divisor of 3635)
...
3635 / 59 = 61.610169491525 (the remainder is 36, so 59 is not a divisor of 3635)
3635 / 60 = 60.583333333333 (the remainder is 35, so 60 is not a divisor of 3635)