What are the divisors of 3615?

1, 3, 5, 15, 241, 723, 1205, 3615

There is a total of 8 positive divisors.
The sum of these divisors is 5808.
The arithmetic mean is 726.

8 odd divisors

1, 3, 5, 15, 241, 723, 1205, 3615

How to compute the divisors of 3615?

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 3615 by each of the numbers from 1 to 3615 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)

3615 / 1 = 3615 (the remainder is 0, so 1 is a divisor of 3615)
3615 / 2 = 1807.5 (the remainder is 1, so 2 is not a divisor of 3615)
3615 / 3 = 1205 (the remainder is 0, so 3 is a divisor of 3615)
...
3615 / 3614 = 1.0002767017156 (the remainder is 1, so 3614 is not a divisor of 3615)
3615 / 3615 = 1 (the remainder is 0, so 3615 is a divisor of 3615)

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 3615 (i.e. 60.12487006223). 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 $\frac{N}{d} = D$ )

3615 / 1 = 3615 (the remainder is 0, so 1 and 3615 are divisors of 3615)
3615 / 2 = 1807.5 (the remainder is 1, so 2 is not a divisor of 3615)
3615 / 3 = 1205 (the remainder is 0, so 3 and 1205 are divisors of 3615)
...
3615 / 59 = 61.271186440678 (the remainder is 16, so 59 is not a divisor of 3615)
3615 / 60 = 60.25 (the remainder is 15, so 60 is not a divisor of 3615)