Question

How do you write the sum of the number \[56+64\] as the product of their GCF and their other sum?

Answer 1

Hint: From the question given, we have been asked to write the sum of the number \[56+64\] as the product of their GCF and another sum. To solve this, first we have to find the GCF of the numbers \[56\text{ and 64}\]. Then by using that, we have to write the given number as the product of the obtained GCF and another sum.

Complete step by step answer:
For answering this question we need to write the sum of the number \[56+64\] as the product of their GCF and another sum.
First we have to find the GCF of the two numbers.
In this process, first we have to find the factors of \[56\].
Factors of \[56\] are \[1,2,4,7,8,14,28,56\]
Now, we have to find the factors of \[64\].
Factors of \[64\] are \[1,2,4,8,16,32,64\]
We can clearly observe that the greatest common factor among them is \[8\].
Therefore, the GCF of the numbers \[56\text{ and 64}\] is \[8\].
We already know that, \[8\] goes into \[56\] exactly \[7\] times.
The number \[8\] goes into \[64\] exactly \[8\] times.
Now, we have to write it as the product of the GCF obtained above and another sum.
Therefore,
\[56+64=8\left( 8 \right)+8\left( 7 \right)\]
\[56+64=8\left( 7+8 \right)\]

Hence, \[56+64\] is written as the product of the GCF obtained and another sum.

Note: We should be well aware of finding the greatest common factor of the given two numbers. Also we should be very careful while finding the factors of the given two numbers. Also, we should be very careful while writing the given number as a product of the GCF obtained and another sum. We should be very careful while finding another sum. Similarly we can find the GCF or LCM of any numbers for suppose $8$ and $16$ the GCF is $8$ and the LCM is $16$ .