Question

What is the GCF of $-10{{c}^{2}}d$ and $15c{{d}^{2}}$?

Answer 1

Hint: The greatest number that is a factor of two or more other numbers and when we find all the factors of two or more numbers and some factors are the same or common, then the largest of those common factors is the greatest common factor.

Complete step by step solution:
Greatest common factor is abbreviated as GCF and is also known as highest common factor.
Now, according to the given question we can rewrite each term as:
In order to find the greatest common factors of the given terms what we need to do basically is to find the factors of the first and second term and then need to find the terms that are common in factors of every term.
$\begin{align}
  & -10{{c}^{2}}d=-2\times 5\times c\times c\times d \\
 & 15c{{d}^{2}}=3\times 5\times c\times d\times d \\
\end{align}$
Now, we need to write the common terms on one side and we do not have any use of other numbers or factors that are individually present or we can say which are not common and then we multiply all those common terms and then what we get is exactly what we need in this question.
Now, we can clearly see that 5, c and d are present in both the terms. So, the greatest common factor GCF of the given terms is $5cd$.
Hence, we can say that GCD of $-10{{c}^{2}}d$ and $15c{{d}^{2}}$ is $5cd$.

Note: Most of the time we get confused that we need to multiply the common terms as many times terms are there or only once. So, the answer to this kind of confusion is yes. In general, the GCD is the number or answer that we get after multiplying the common terms is the greatest common factor of the different terms.