Which equation shows how to rewrite the sum of 42 and 54 using their greatest common factor?
A. 54+42=6(9)+2(14)
b. 54+42=3(18+14)
c. 54+42=4(8)(3)
d. 54+42=6(9+7)
d. 54+42=6(9+7)
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To rewrite the sum of 42 and 54 using their greatest common factor, we need to find the greatest common factor (GCF) of 42 and 54. The GCF is the largest number that divides both 42 and 54 evenly.
To find the GCF, we can start by finding the prime factors of each number. The prime factors of 42 are 2, 3, and 7, while the prime factors of 54 are 2, 3, and 3.
The GCF is the product of the common prime factors raised to the lowest exponent. In this case, the common prime factors are 2 and 3, and the lowest exponent is 1 for both primes. Therefore, the GCF of 42 and 54 is 2 * 3 = 6.
Now, let's go through the given options to see which equation shows how to rewrite the sum of 42 and 54 using their greatest common factor.
Option A: 54 + 42 = 6(9) + 2(14)
In this equation, we have rewritten 42 as the product of the GCF (6) and 7, and 54 as the product of the GCF (6) and 9. This equation correctly represents the sum of 42 and 54 using their greatest common factor.
Option B: 54 + 42 = 3(18 + 14)
In this equation, we have rewritten the sum of 42 and 54 as the product of the GCF (3) and the sum of 18 and 14. This equation does not use the greatest common factor to rewrite the individual numbers, so it doesn't represent the sum of 42 and 54 using their greatest common factor.
Option C: 54 + 42 = 4(8)(3)
In this equation, we have rewritten 42 as the product of the GCF (4) and 3, and 54 as the product of the GCF (4) and 8. This equation does not correctly represent the sum of 42 and 54 using their greatest common factor.
Option D: 54 + 42 = 6(9 + 7)
In this equation, we have rewritten the sum of 42 and 54 as the product of the GCF (6) and the sum of 9 and 7. This equation correctly represents the sum of 42 and 54 using their greatest common factor.
Therefore, the equation that shows how to rewrite the sum of 42 and 54 using their greatest common factor is A. 54 + 42 = 6(9) + 2(14).