What are the divisors of 6013?

1, 7, 859, 6013

There is a total of 4 positive divisors.
The sum of these divisors is 6880.
The arithmetic mean is 1720.

4 odd divisors

1, 7, 859, 6013

How to compute the divisors of 6013?

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 6013 by each of the numbers from 1 to 6013 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)

6013 / 1 = 6013 (the remainder is 0, so 1 is a divisor of 6013)
6013 / 2 = 3006.5 (the remainder is 1, so 2 is not a divisor of 6013)
6013 / 3 = 2004.3333333333 (the remainder is 1, so 3 is not a divisor of 6013)
...
6013 / 6012 = 1.0001663339987 (the remainder is 1, so 6012 is not a divisor of 6013)
6013 / 6013 = 1 (the remainder is 0, so 6013 is a divisor of 6013)

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 6013 (i.e. 77.543536158728). 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 $\frac{N}{d} = D$ )

6013 / 1 = 6013 (the remainder is 0, so 1 and 6013 are divisors of 6013)
6013 / 2 = 3006.5 (the remainder is 1, so 2 is not a divisor of 6013)
6013 / 3 = 2004.3333333333 (the remainder is 1, so 3 is not a divisor of 6013)
...
6013 / 76 = 79.118421052632 (the remainder is 9, so 76 is not a divisor of 6013)
6013 / 77 = 78.090909090909 (the remainder is 7, so 77 is not a divisor of 6013)