What are the divisors of 6015?

1, 3, 5, 15, 401, 1203, 2005, 6015

There is a total of 8 positive divisors.
The sum of these divisors is 9648.
The arithmetic mean is 1206.

8 odd divisors

1, 3, 5, 15, 401, 1203, 2005, 6015

How to compute the divisors of 6015?

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 6015 by each of the numbers from 1 to 6015 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)

6015 / 1 = 6015 (the remainder is 0, so 1 is a divisor of 6015)
6015 / 2 = 3007.5 (the remainder is 1, so 2 is not a divisor of 6015)
6015 / 3 = 2005 (the remainder is 0, so 3 is a divisor of 6015)
...
6015 / 6014 = 1.0001662786831 (the remainder is 1, so 6014 is not a divisor of 6015)
6015 / 6015 = 1 (the remainder is 0, so 6015 is a divisor of 6015)

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 6015 (i.e. 77.556431067965). 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 $\frac{N}{d} = D$ )

6015 / 1 = 6015 (the remainder is 0, so 1 and 6015 are divisors of 6015)
6015 / 2 = 3007.5 (the remainder is 1, so 2 is not a divisor of 6015)
6015 / 3 = 2005 (the remainder is 0, so 3 and 2005 are divisors of 6015)
...
6015 / 76 = 79.144736842105 (the remainder is 11, so 76 is not a divisor of 6015)
6015 / 77 = 78.116883116883 (the remainder is 9, so 77 is not a divisor of 6015)