Question
(4) Listen Factor the expression using the GCF. \( 16 x+56 y=\square \)
Ask by Curry Pierce. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression 16x + 56y factored using the GCF is 8(2x + 7y).
Solution
To factor the expression 16x + 56y using the Greatest Common Factor (GCF), first determine the GCF of 16 and 56.
1. The factors of 16 include 1, 2, 4, 8, 16.
2. The factors of 56 include 1, 2, 4, 7, 8, 14, 28, 56.
3. The largest common factor is 8.
Now, factor 8 out of the expression:
16x + 56y = 8(2x + 7y).
Thus, the factored form is 8(2x + 7y).
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Simplify this solution Mind Expander
To factor the expression \( 16x + 56y \) using the GCF (Greatest Common Factor), we first need to determine the GCF of the coefficients. The GCF of 16 and 56 is 8. So, we can factor out 8 from both terms: \( 16x + 56y = 8(2x + 7y) \). Now, we’ve successfully factored the expression! If you want to impress your friends with some math magic, you can always revisit the GCF process! Identify the smallest powers of all prime factors in the coefficients. For example, both 16 and 56 share prime factors: 2 (as \(16 = 2^4\) and \(56 = 2^3 \times 7\)). Remember, recognizing these patterns makes factoring a lot more fun and less like a chore!
