Question

How do you write the sum of the number \[49 + 63\] as the product of their GCF and another sum?

Answer 1

Hint: We have to find the sum of the number \[49 + 63\]as the product of their GCF and another sum.
First, we will factorize the numbers.
After factoring, we will find the GCF of 49 and 63.
We will take the GCF as a common term and proceed as we need.

Complete step-by-step solution:
It is given that; \[49 + 63\]
We have to write the sum of the number \[49 + 63\] as the product of their GCF and another sum.
First, we will factorize the numbers.
So, we have,
\[49 = 7 \times 7\]
And, \[63 = 7 \times 3 \times 3\]
GCF of \[49,63\] is \[7\].
\[49 + 63\] can be written as,
\[49 + 63 = 7 \times 7 + 7 \times 3 \times 3\]
We will take 7 as common,
\[49 + 63 = 7 \times (7 + 3 \times 3)\]
Simplifying we get,
\[49 + 63 = 7 \times (7 + 9)\]
Simplifying again we get,
\[49 + 63 = 7 \times 16\]
Simplifying again we get,
\[49 + 63 = 112\]
Hence, the sum of \[49 + 63\] is \[112\].

Note: In Mathematics, a factor is a number which when multiplied by other numbers to get the desired numbers. The resulting number is also known as factors. The largest number, which is the factor of two or more numbers is called the Greatest Common Factor (GCF). It is the largest number (factor) that divides them resulting in a natural number.
Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor.
The GCF is also known as the Highest Common Factor (HCF).