Question

How do you find the highest common factors for \[6\] and \[12\]?

Answer 1

Hint: For finding the highest common factor of a given pair of numbers, we first have to list down all of the factors of both the numbers of the given pair. Then on comparing the factors of both the numbers, we can list down all of the factors which are common to both of them. Finally, the common factor which will be the highest will be the required highest common factor for the given pair of numbers.

Complete step-by-step solution:
For determining the highest common factor for the numbers \[6\] and \[12\], we first have to write the factors for these numbers.
We know that the number \[6\] can be written as
\[6 = 1 \times 6 = 1 \times 2 \times 3\]
So the factors of the number \[6\] are \[1,2,3,6\].
Now, we know that the number \[12\] can be written as
\[\begin{array}{l}12 = 1 \times 12\\ \Rightarrow 12 = 1 \times 4 \times 3\\ \Rightarrow 12 = 1 \times 2 \times \,2 \times 3\end{array}\]
So the factors of the number \[12\] are \[1,2,3,4,6,12\].
From the factors of the numbers \[6\] and \[12\], we note the factors common among them to be \[1,2,3,6\].
As can be clearly observed, the highest factor of the above common factors is equal to \[6\].

Hence, the highest common factor for \[6\] and \[12\] is equal to \[6\].

Note: We must note that we have to write all the factors of each number, starting from one to the number itself. We do not have to note the prime factors of each number. This is because the highest common factor need not be a prime number. Also, we can see that the number \[6\] is a perfect divisor of the number \[12\]. So we could directly conclude that the highest common factor for \[6\] and \[12\] is equal to \[6\].