What are the divisors of 6010?

1, 2, 5, 10, 601, 1202, 3005, 6010

There is a total of 8 positive divisors.
The sum of these divisors is 10836.
The arithmetic mean is 1354.5.

4 even divisors

2, 10, 1202, 6010

4 odd divisors

1, 5, 601, 3005

How to compute the divisors of 6010?

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 6010 by each of the numbers from 1 to 6010 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)

6010 / 1 = 6010 (the remainder is 0, so 1 is a divisor of 6010)
6010 / 2 = 3005 (the remainder is 0, so 2 is a divisor of 6010)
6010 / 3 = 2003.3333333333 (the remainder is 1, so 3 is not a divisor of 6010)
...
6010 / 6009 = 1.0001664170411 (the remainder is 1, so 6009 is not a divisor of 6010)
6010 / 6010 = 1 (the remainder is 0, so 6010 is a divisor of 6010)

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 6010 (i.e. 77.524189773257). 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 $\frac{N}{d} = D$ )

6010 / 1 = 6010 (the remainder is 0, so 1 and 6010 are divisors of 6010)
6010 / 2 = 3005 (the remainder is 0, so 2 and 3005 are divisors of 6010)
6010 / 3 = 2003.3333333333 (the remainder is 1, so 3 is not a divisor of 6010)
...
6010 / 76 = 79.078947368421 (the remainder is 6, so 76 is not a divisor of 6010)
6010 / 77 = 78.051948051948 (the remainder is 4, so 77 is not a divisor of 6010)