Question

How do you write the sum of the number $63 + 15$as the product of their GCF and another sum?

Answer 1

Hint: Given the expression. We have to write this expression as the product of their GCF and another sum. First, we will find the prime factors of both the terms in the expression. Then, find the greatest common factor which is equal to the highest prime factor which is common in the factors of both terms. Then we will write both the terms by multiplying a certain number with the GCF.

Complete step by step answer:
We are given the expression. First we will find the prime factors of the term $63$.
$63 = 3 \times 3 \times 7$
Now, we will find the prime factors of the term $15$.
$ \Rightarrow 15 = 3 \times 5$
Now, find the common factor to both of these terms.
\[GCF = 3\]
Now, we will rewrite the given expression as a product of GCF and other numbers.
$ \Rightarrow 63 + 15 = 3 \times 21 + 3 \times 5$
Now, we will take out the common term.
$ \Rightarrow 3 \times \left( {21 + 5} \right)$
Now, the expression is represented as a product of GCF $3$ and another sum$\left( {21 + 5} \right)$.
We can check the result by comparing the result of the given expression and result of the expression $3 \times \left( {21 + 5} \right)$.
\[ \Rightarrow 63 + 15 = 3 \times \left( {21 + 5} \right)\]
\[ \Rightarrow 78 = 3 \times 26\]
\[ \Rightarrow 78 = 78\]
Here, the value of LHS is equal to the value of RHS, which means the resultant expression is correct.

Hence the expression can be written as $3 \times \left( {21 + 5} \right)$

Additional information:
The GCF of two numbers is equal to the common prime factors of both the numbers. The prime factors of the number are the numbers that can divide the number without leaving a remainder.

Note: In such types of questions students mainly do mistakes while finding the factors of the numbers. Then, students may get confused while finding the GCF of the numbers and write the given expression using the GCF of the expression.