How do you write 30 + 5430+54 as the sum of two numbers times their GCF?

2 Answers
smendyka
Oct 10, 2017

See a solution process below:

Explanation:

Find the prime factors for each number as:

30 = 2 xx 3 xx 530=2×3×5

54 = 2 xx 3 xx 3 xx 354=2×3×3×3

Now identify the common factors and determine the GCF:

30 = color(red)(2) xx color(red)(3) xx 530=2×3×5

54 = color(red)(2) xx color(red)(3) xx 3 xx 354=2×3×3×3

Therefore:

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

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

(color(red)(6) xx 5) + (color(red)(6) xx 9) =>(6×5)+(6×9)⇒

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

SCooke
Oct 10, 2017

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

Explanation:

First, we find their Greatest Common Factor:
30 = 2 xx 3 xx 530=2×3×5
54 = 2 xx 3 xx 3 xx 354=2×3×3×3
GCF = 6GCF=6

The sum of the two numbers is 30 + 54 = 8430+54=84
Divide by the GCF to get a multiplicative factor easily:

84/6 = 14846=14 We convert 1414 into a simple sum:
14 = 7 + 714=7+7 and then combine them into the final expression.
84 = 6 xx (7 + 7)84=6×(7+7)

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