Question

How do find the greatest common factor of \[39v,30uv\]?

Answer 1

Hint: From the question we have been asked to find the greatest common factor of given two elements. For solving these types of questions we will take the help of the definition of greatest common factor or simply GCF. We will factorise the given two terms in the question and apply the GCF and find the required solution to the question.

Complete step by step answer:
Now, as we mentioned in the above we will factorise the two terms given in the question. So, we get the factorisation of the terms as follows.
The factorisation of the term \[39v\] will be as follows.
\[\Rightarrow 39v=3\times 13\times v\]
Now, we will factorise the second term given in the question which is \[30uv\].
So, the factorisation of \[30uv\] will be as follows.
\[\Rightarrow 30uv=2\times 3\times 5\times u\times v\]
Now, we know that from the definition of the GCF which is when we take two numbers then the GCF will be the greatest factor which is a factor of both the numbers or simply the largest of the common factors is known as the greatest common factor.
So, here for the two numbers we got the factorisation.
Now, all the common factors when multiplied together gives us the greatest common factor. So, we get,
\[\Rightarrow 3\times v\]

Therefore, the greatest common factor will be \[3v\].

Note: Students should be very careful in doing the factorisation accurately because if we miss any factor it will make our solution wrong. Here if we take only the \[3\] as GCF then our solution will be wrong. We should take both the common factors and multiply them, so our answer will be \[3v\].