How to Find the Greatest Common Factor of Monomials

TL;DR

To find the greatest common factor of monomials, break each term into its prime factors and identify the overlapping factors among them. For example, in the monomials 10cd², 5cd, and 25c³d², the greatest common factor is 5cd, as these are the shared factors across all expressions.

Transcript

Find the greatest common factor of these monomials. And when they say monomials, that's just a fancy word for saying a one term expression. Each of these only, obviously, have one term in them. Now to find the greatest common factor of these, the way I think about it is, I like to break up each of these terms into their constituent parts. Make them... Read More

Key Insights

• 😑 Monomials are one-term expressions, and finding their greatest common factor involves breaking them down into constituent parts.
• 🧑‍🏭 Numeric coefficients are factored into their prime factors, while variables are written with their minimum exponents.
• 🧑‍🏭 The greatest common factor of monomials is determined by identifying the factors that overlap in all expressions being compared.

Questions & Answers

Q: What is a monomial?

A monomial is an algebraic expression with only one term. It can include a combination of numbers, variables, and exponents.

Q: How do you break down a monomial into its simplest form?

To break down a monomial into its simplest form, factorize any numeric coefficients into their prime factors and write variables with their minimum exponent.

Q: How do you find the greatest common factor of monomials?

To find the greatest common factor of monomials, break down each term into its simplest constituents and identify the factors that overlap in all expressions.

Q: Can the greatest common factor be larger than the expressions themselves?

No, the greatest common factor cannot be larger than the expressions being compared. It represents the largest factor that overlaps in all monomials.

Summary & Key Takeaways

• Monomials are one-term expressions, and to find their greatest common factor, break down each term into its prime factors.

• The video demonstrates breaking down three monomials (10cd^2, 5cd, 25c^3d^2) into their simplest constituents.

• The greatest common factor of these monomials is found by identifying the factors that overlap in all three expressions (5cd).