Factor the expression using the GCF.
60 – 36 =
The Correct Answer and Explanation is :
To factor the expression ( 60 – 36 ) using the Greatest Common Factor (GCF), we follow these steps:
Step 1: Identify the GCF of 60 and 36
First, we need to find the greatest common factor (GCF) of the two numbers, 60 and 36.
- The factors of 60 are: ( 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 )
- The factors of 36 are: ( 1, 2, 3, 4, 6, 9, 12, 18, 36 )
The greatest factor that both 60 and 36 share is 12.
Step 2: Factor out the GCF
Now, we can factor out 12 from the expression ( 60 – 36 ). We do this by dividing both terms by 12.
[
60 \div 12 = 5 \quad \text{and} \quad 36 \div 12 = 3
]
Thus, we can rewrite the expression as:
[
60 – 36 = 12(5 – 3)
]
Step 3: Verify the factorization
Now let’s verify the factorization by distributing the 12 back:
[
12(5 – 3) = 12 \times 5 – 12 \times 3 = 60 – 36
]
This matches the original expression, so the factorization is correct.
Explanation
The process of factoring involves identifying the greatest common factor (GCF) of the terms in the expression. In this case, both 60 and 36 share a common factor of 12. By factoring out this GCF, we simplify the expression, making it easier to work with. This is a common technique used to simplify algebraic expressions and is especially helpful when working with larger polynomials or terms. Factoring out the GCF not only makes expressions simpler but can also be crucial in solving equations or simplifying problems in higher mathematics.