What are the divisors of 6070?

1, 2, 5, 10, 607, 1214, 3035, 6070

There is a total of 8 positive divisors.
The sum of these divisors is 10944.
The arithmetic mean is 1368.

4 even divisors

2, 10, 1214, 6070

4 odd divisors

1, 5, 607, 3035

How to compute the divisors of 6070?

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 6070 by each of the numbers from 1 to 6070 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)

6070 / 1 = 6070 (the remainder is 0, so 1 is a divisor of 6070)
6070 / 2 = 3035 (the remainder is 0, so 2 is a divisor of 6070)
6070 / 3 = 2023.3333333333 (the remainder is 1, so 3 is not a divisor of 6070)
...
6070 / 6069 = 1.0001647717911 (the remainder is 1, so 6069 is not a divisor of 6070)
6070 / 6070 = 1 (the remainder is 0, so 6070 is a divisor of 6070)

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 6070 (i.e. 77.91020472313). 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 $\frac{N}{d} = D$ )

6070 / 1 = 6070 (the remainder is 0, so 1 and 6070 are divisors of 6070)
6070 / 2 = 3035 (the remainder is 0, so 2 and 3035 are divisors of 6070)
6070 / 3 = 2023.3333333333 (the remainder is 1, so 3 is not a divisor of 6070)
...
6070 / 76 = 79.868421052632 (the remainder is 66, so 76 is not a divisor of 6070)
6070 / 77 = 78.831168831169 (the remainder is 64, so 77 is not a divisor of 6070)