Factor the expression using the GCF. 60 – 36 =
The Correct Answer and Explanation is:
To factor the expression 60−3660 – 3660−36 using the Greatest Common Factor (GCF), let’s break it down step by step.
Step 1: Find the GCF of 60 and 36
To begin, we need to determine the GCF of the two numbers, 60 and 36. The GCF is the largest number that divides both 60 and 36 evenly.
- Prime Factorization of 60:
- 60 can be factored as 60=22×3×560 = 2^2 \times 3 \times 560=22×3×5.
- Prime Factorization of 36:
- 36 can be factored as 36=22×3236 = 2^2 \times 3^236=22×32.
Step 2: Determine the Common Factors
From the factorizations:
- The common factors between 60 and 36 are 222^222 and 333.
- The GCF is therefore 22×3=122^2 \times 3 = 1222×3=12.
Step 3: Factor the Expression Using the GCF
Now, we can factor out the GCF of 12 from the original expression 60−3660 – 3660−36.60−36=12×(6012−3612)60 – 36 = 12 \times \left( \frac{60}{12} – \frac{36}{12} \right)60−36=12×(1260−1236)60−36=12×(5−3)60 – 36 = 12 \times (5 – 3)60−36=12×(5−3)60−36=12×260 – 36 = 12 \times 260−36=12×2
Step 4: Simplify
Thus, the factored form of 60−3660 – 3660−36 is:60−36=12×2=2460 – 36 = 12 \times 2 = 2460−36=12×2=24
Explanation:
The process of factoring out the GCF involves finding the largest number that divides both terms in the expression. By recognizing that both 60 and 36 share a common factor of 12, we can simplify the expression and rewrite it as the product of 12 and the difference between 5 and 3, which is 2. This method helps in simplifying expressions, making it easier to handle mathematical problems and calculations.
