Question

How do you write the sum of the number $30 + 54$ as the product of their GCF and another sum?

Answer 1

Hint: GCF, greatest common factor, is the greatest factor that divides two numbers. To find the GCF of two numbers, list the prime of each number, multiply those factors of both numbers in common. If there are no common prime factors, the GCF is 1. The greatest common factor (GCF), of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder.

Complete step-by-step solution:
Here given the sum of two numbers. The two numbers are 30 and 54.
Now in order to find the HCF of the sum of these numbers, first we have to find the HCF of each of the numbers separately.
To find the HCF of each number separately, we have to factorize the given number.
Now factoring the number 30, as given below:
$ \Rightarrow 30 = 5 \times 6$
$ \Rightarrow 30 = 5 \times 2 \times 3$
Now factoring the number 54, as given below:
$ \Rightarrow 30 = 6 \times 9$
$ \Rightarrow 30 = 2 \times 3 \times 3 \times 3$
Now the sum of the numbers 30 and 54, is given by:
$ \Rightarrow 30 + 54$
$ \Rightarrow \left( {5 \times 2 \times 3} \right) + \left( {2 \times 3 \times 3 \times 3} \right)$
$ \Rightarrow \left( {5 \times 6} \right) + \left( {6 \times 9} \right)$
Taking the number 6 common from the terms, as given below:
$ \Rightarrow 6 \times \left( {5 + 9} \right)$
$\therefore 30 + 54 = 6 \times \left( {5 + 9} \right)$
Here the GCF of $30 + 54$ is $6$.

$30 + 54 = 6 \times \left( {5 + 9} \right)$, where 6 is the HCF of both 30 and 54.

Note: Please note that GCF is also often called HCF, highest common factor, and also known as GCD, greatest common divisor. In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the common divisor of x and y is denoted.