1 / 17

Understanding the Greatest Common Factor (GCF) with Examples and Applications

The Greatest Common Factor (GCF) is the largest number that divides two or more integers without leaving a remainder. This guide provides definitions, examples, and applications of GCF in both numerical and polynomial contexts. Learn how to determine the GCF of natural numbers, explore its significance in factoring polynomials, and understand its role in identifying relatively prime numbers. With step-by-step examples, students will gain a clear understanding of GCF and how to utilize it effectively in mathematical problems and homework.

tiger
Télécharger la présentation

Understanding the Greatest Common Factor (GCF) with Examples and Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. GCFWhat does it stand for? What is it?

  2. What do these have in common?? ALL FLY

  3. What do these have in common?? ALL ANIMALS

  4. The greatest common factor (GCF) of two natural numbers is the largest number that is a factor of both numbers.Example: 84= 2 x 2 x 3 x 7 100= 2 x 2 x 5 x 5 GCF = 2 x 2 = 4

  5. Find the GCF of 84 and 180. 84= 2 x 2 x 3 x 7 180= 2 x 2 x 3 x 3 x 5 GCF = 2 x 2 x 3 = 12

  6. Find the GCF of 21 and 10. 21=3 x 7 10=2 x 5 GCF = 1 If two integers have no common prime factors, their GCF is 1. Such numbers are said to be relatively prime.

  7. GCF with Variables Note: With variables, the GCF will always be the smallest exponent of a common variable Examples: 12x3 and 16x2 45a5, 50a7 GCF = 4x2 GCF = 5a5

  8. What is the greatest common factor?? 5a 35 The number 5

  9. What is the greatest common factor?? 3y -8xy y

  10. What is the greatest common factor?? -11x 22x2 11x Note: With negatives, go by the leading term!!

  11. What is the greatest common factor?? -4x6-x4-2x2 -x2 Note: With negatives, go by the leading term!!

  12. FACTORING POLYNOMIALS • Factoring = Write the polynomial as a product. • STEPS: • 1) Find the GCF of all its terms. • 2) Write the polynomial as a product by factoring out the GCF from all the terms. • - This is done by dividing the original terms of the polynomial by the GCF. • 3) The remaining factors in each term will form a polynomial.

  13. Example 1 4x + 6y What is the GCF? 2 Factor out the GCF 2(2x + 3y)

  14. Example 2 6x3 – 9x2 + 12x What is the GCF? 3x Factor out the GCF 3x(2x2 – 3x + 4)

  15. You try: Factor 1. 16x2 – 8x What is their GCF? – 1 = 8x( ) 2x 2. 2a3 – 6a = 2a( ) a2 – 3

  16. Factor 3. 2h2k + 2k What is their GCF? = 2k( ) + 1 h2 4. 6uv + 9v2 = 3v( ) 2u + 3v

  17. Homeworkpg. 417 #4 to 50 even

More Related