What are the divisors of 3695?

1, 5, 739, 3695

There is a total of 4 positive divisors.
The sum of these divisors is 4440.
The arithmetic mean is 1110.

4 odd divisors

1, 5, 739, 3695

How to compute the divisors of 3695?

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 3695 by each of the numbers from 1 to 3695 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)

3695 / 1 = 3695 (the remainder is 0, so 1 is a divisor of 3695)
3695 / 2 = 1847.5 (the remainder is 1, so 2 is not a divisor of 3695)
3695 / 3 = 1231.6666666667 (the remainder is 2, so 3 is not a divisor of 3695)
...
3695 / 3694 = 1.0002707092583 (the remainder is 1, so 3694 is not a divisor of 3695)
3695 / 3695 = 1 (the remainder is 0, so 3695 is a divisor of 3695)

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 3695 (i.e. 60.786511661717). 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 $\frac{N}{d} = D$ )

3695 / 1 = 3695 (the remainder is 0, so 1 and 3695 are divisors of 3695)
3695 / 2 = 1847.5 (the remainder is 1, so 2 is not a divisor of 3695)
3695 / 3 = 1231.6666666667 (the remainder is 2, so 3 is not a divisor of 3695)
...
3695 / 59 = 62.627118644068 (the remainder is 37, so 59 is not a divisor of 3695)
3695 / 60 = 61.583333333333 (the remainder is 35, so 60 is not a divisor of 3695)