How do you write #30 + 54# as the sum of two numbers times their GCF?

2 Answers
Oct 10, 2017

See a solution process below:

Explanation:

Find the prime factors for each number as:

#30 = 2 xx 3 xx 5#

#54 = 2 xx 3 xx 3 xx 3#

Now identify the common factors and determine the GCF:

#30 = color(red)(2) xx color(red)(3) xx 5#

#54 = color(red)(2) xx color(red)(3) xx 3 xx 3#

Therefore:

#"GCF" = color(red)(2) xx color(red)(3) = 6#

Now, we can factor #color(red)(6)# from each number giving:

#(color(red)(6) xx 5) + (color(red)(6) xx 9) =>#

#color(red)(6)(5 + 9)#

Oct 10, 2017

#84 = 6 xx (7 + 7)#
Or, completely written out:
#30 + 54 = 6 xx (7 + 7)#

Explanation:

First, we find their Greatest Common Factor:
#30 = 2 xx 3 xx 5#
#54 = 2 xx 3 xx 3 xx 3#
#GCF = 6#

The sum of the two numbers is #30 + 54 = 84#
Divide by the GCF to get a multiplicative factor easily:

#84/6 = 14# We convert #14# into a simple sum:
#14 = 7 + 7# and then combine them into the final expression.
#84 = 6 xx (7 + 7)#