Find the greatest common factor of 8a3b2 and 12ab4 – In mathematics, finding the greatest common factor (GCF) of two or more algebraic expressions is a fundamental operation that plays a crucial role in simplifying and solving complex expressions. This article delves into the process of finding the GCF of 8a3b2 and 12ab4, providing a step-by-step guide, examples, and practical applications.
The GCF, also known as the greatest common divisor (GCD), is the largest factor that divides evenly into two or more numbers. In this case, we will determine the GCF of 8a3b2 and 12ab4, two algebraic expressions with variables and numerical coefficients.
Greatest Common Factor of 8a3b2 and 12ab4: Find The Greatest Common Factor Of 8a3b2 And 12ab4
The greatest common factor (GCF) of two or more algebraic expressions is the largest algebraic expression that is a factor of all the given expressions. In this case, we need to find the GCF of 8a 3b 2and 12ab 4.
Factorization, Find the greatest common factor of 8a3b2 and 12ab4
First, we factor each expression into its prime factors:
- 8a 3b 2= 2 3– a 3– b 2
- 12ab 4= 2 2– 3 – a – b 4
Identifying Common Factors
The common prime factors in both factorizations are 2, a, and b 2.
GCF Calculation
The GCF is the product of the common prime factors:
GCF = 2 – a – b 2= 2ab 2
Example
For example, the GCF of 16a 5b 3and 24a 2b 5is:
- 16a 5b 3= 2 4– a 5– b 3
- 24a 2b 5= 2 3– 3 – a 2– b 5
The common prime factors are 2, a 2, and b 3, so the GCF is:
GCF = 2 – a 2– b 3= 2a 2b 3
FAQs
What is the greatest common factor?
The greatest common factor (GCF) is the largest factor that divides evenly into two or more numbers.
How do I find the GCF of two algebraic expressions?
To find the GCF of two algebraic expressions, factor both expressions into their prime factors, identify the common prime factors, and multiply them together.
What are the applications of GCF?
GCF has various applications in mathematics, including simplifying algebraic expressions, solving equations, and finding the least common multiple (LCM).
