4 2 . Greatest Common Factor In the Real World

Slides:

Advertisements

Similar presentations

Section 5.1 Prime Factorization and Greatest Common Factor.

Advertisements

EXAMPLE 2 Identifying Relatively Prime Numbers Tell whether the numbers 112 and 45 are relatively prime. SOLUTION Write the prime factorization of each.

Begin by writing the prime factorization of each number.

Multiple A multiple of a number is the product of that number and any other whole number. Zero is a multiple of every number. What am I? Examples: 4: 8,

Sub Title Factors and Multiples Chapter 3: Conquering SAT Math.

EXAMPLE 1 Making a List to Find the GCF An orchestra conductor divides 48 violinists, 24 violists, and 36 cellists into ensembles. Each ensemble has the.

To Start: 10 Points!!! Simplify and Evaluate: (-4)5 =(-4)(-4)(-4)(-4)(-4) = -4,096!! 2x3 + 4y, for x=-3 and y=2 2(-3)3 + 4(2) 2(-27) !!!!

EXAMPLE 2 Identifying Equivalent Fractions

Least Common Multiple (LCM) of

4-2 GCF Greatest Common Factor (GCF) - The largest factor that is the same for a given set of numbers Two methods: 1.) Listing Method or modified listing.

Greatest Common Factor Objective: Finding Greatest Common Factor (GCF) VocabularyThe greatest common factor is the biggest factor that is common to two.

4-2 Greatest Common Factor Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day.

Greatest Common Factors a.k.a. GCF

Greatest Common Factor

EXAMPLE 4 Finding the GCF of Monomials

GREATEST COMMON FACTOR

Reducing Fractions By: Greg Stark EC&I 831 What is meant by reducing fractions? To reduce a fraction means that we find an equivalent fraction that has.

Greatest Common Factor

Factors, Primes & Composite Numbers

Finding Factors Section What are factors? Factors are numbers that can be divided evenly into a larger number called a product. Example:1, 2, 3,

Warm UP Step 1: Write the whole numbers from 2 through 48. Step 2: Circle 2 and cross out all multiples of 2 other than 2 (the first row below is shown.

Objectives The student will be able to:

Multiples, Factors, Primes & Composite Numbers

 What prime factorization is.  For example the prime factorization of 24 = 2223  Today we will learn how to find the greatest common factor of two.

EXAMPLE 1 Finding the Greatest Common Factor Find the greatest common factor of 56 and 84. SOLUTION STEP 1 Write the prime factorization of each number.

Simplifying Fractions

OBJ: to find the greatest common factor of two or more numbers.

Factoring using GCF interpret parts of an expressions such as terms, factors, and coefficient.

Factoring using GCF interpret parts of an expressions such as terms, factors, and coefficient.

Chapter 4 Jeopardy Divisibility and factors Prime Factorization GCF Simplify Fractions Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400.

Goal: Find the greatest common factor of two or more numbers.

DO NOW Complete in your notebook/binder: 1)7 + 5 * 8 2)-6 +(-2) ÷ 4 3)| | 4)Write down the difference between a prime and a composite number.

Factors Divisibility Lesson 6Power Up BPage 40. Factors ›A whole number that divides evenly into another whole number. ›List the factors of 27. ›1, 3,

Carol Chervenak Finding the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) using Prime Factorization! No need to make lists like you.

Chapter 11 Review Math. Tell whether the following numbers are divisible by 2, 3, 4, 5, 6, 8, 9, 10, and ,488 1,881 3,360.

Using the GCF to Solve Problems ANSWER The most groups that can be formed is 12. Dividing the number of each type of musician by 12, you find each group.

Defining Success Lesson 14-Finding the Greatest Common Factor Problem Solved!

Factors and the Greatest Common Factor

Unit 1 Test Review. 1-2 Exponents 1) Write the expression in exponential form 2 x 2 x 2 x 2 x 2 2) Find the value of.

§5.4 Part 1 GCF Objectives: - Factor out the GCF of an expression.

Finding the Greatest Common Factor. The greatest common factor of two or more numbers is the greatest number that is a factor of every number.

Extra Lesson Greatest Common Factor and Least Common Multiple of Monomials Essential Question: How do you find the greatest common factor and least common.

PRIME FACTORIZATION Pg. 12. ESSENTIAL QUESTION HOW do you use equivalent rates in the real world?

Finding Greatest Common Factor

Greatest Common Factor

Greatest Common Factor

8 Greatest Common Factor

How to Find the Greatest Common Factor (GCF) in 5 Steps

Introduction to Factoring

GCF (greatest common factor) & LCM (least common multiple)

Warm Up 1. 50, , 7 3. List the factors of 28. no yes

Positive Numbers and the Number Line

GCF (greatest common factor) & LCM (least common multiple) Click on the link below to access videos:

Finding the Greatest Common Factor

8 Greatest Common Factor

Positive Numbers and the Number Line

Prime Factorization Course

Determining Factors and Multiples

Factors and the Greatest Common Factor

Least common multiple Lesson 1.3.

Objectives The student will be able to:

Greatest Common Factor

Finding the Greatest Common Factor (GCF)

Greatest Common Factor

Warm Up Tell whether the number is prime or composite. If it is composite, write its prime factorization using exponents Factor the monomial

Section 2-1 Factors.

Greatest Common Factor

Greatest Common Factor GCF

Finding the Greatest Common Factor (GCF)

Presentation transcript:

4 2 . Greatest Common Factor In the Real World L E S S O N 4 2 . Greatest Common Factor In the Real World Orchestra An orchestra conductor divides 48 violinists, 24 violists, and 36 cellists into ensembles. Each ensemble has the same number of each instrument. What is the greatest number of ensembles that can be formed? How many violinists, violists, and cellists will be in each ensemble?

4 2 . Greatest Common Factor In the Real World L E S S O N 4 2 . Greatest Common Factor In the Real World Orchestra An orchestra conductor divides 48 violinists, 24 violists, and 36 cellists into ensembles. Each ensemble has the same number of each instrument. What is the greatest number of ensembles that can be formed? How many violinists, violists, and cellists will be in each ensemble? A whole number that is a factor of two or more nonzero whole numbers is called a common factor. The greatest of the common factors is called the greatest common factor (GCF). One way to find the greatest common factor of two or more numbers is to make a list of all the factors of each number and identify the greatest number that is on every list.

4 2 . 1 Greatest Common Factor Making a List to Find the GCF L E S S O N 4 2 . EXAMPLE 1 Making a List to Find the GCF In the previous slide, the greatest number of ensembles that can be formed is given by the greatest common factor of 48, 24, and 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 1, 2, 3, 4, 6, 12 The common factors are 1, 2, 3, 4, 6, and 12. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 3, 4, 6, 12 The GCF is 12. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 1, 2, 3, 4, 6, 12 ANSWER The greatest common factor of 48, 24, and 36 is 12. So, the greatest number of ensembles that can be formed is 12. Then each ensemble will have 4 violinists, 2 violists, and 3 cellists.

4 2 . Greatest Common Factor Using Prime Factorization L E S S O N 4 2 . Using Prime Factorization Another way to find the greatest common factor of two or more numbers is to use the prime factorization of each number. The product of the common prime factors is the greatest common factor.

4 2 . 2 Greatest Common Factor L E S S O N 4 2 . EXAMPLE 2 Using Prime Factorization to Find the GCF Find the greatest common factor of 180 and 126 using prime factorization. Begin by writing the prime factorization of each number. 180 10  18 2  5  2  9 2  5  2  3  3 126 2  63 2  3  21 2  3  3  7 180 = 2  2  3  3  5 126 = 2  3  3  7

4 2 . 2 Greatest Common Factor L E S S O N 4 2 . EXAMPLE 2 Using Prime Factorization to Find the GCF Find the greatest common factor of 180 and 126 using prime factorization. Begin by writing the prime factorization of each number. 180 10  18 2  5  2  9 2  5  2  3  3 126 2  63 2  3  21 2  3  3  7 180 = 2  2  3  3  5 126 = 2  3  3  7 The common prime factors of 180 and 126 are 2, 3, and 3. ANSWER So, the greatest common factor is 2  3 2 = 18.

4 2 . Greatest Common Factor L E S S O N 4 2 . Relatively Prime Two or more numbers are relatively prime if their greatest common factor is 1.

4 2 . 3 Greatest Common Factor L E S S O N 4 2 . Relatively Prime Two or more numbers are relatively prime if their greatest common factor is 1. EXAMPLE 3 Identifying Relatively Prime Numbers Tell whether the numbers are relatively prime. 15, 51 28, 45 Factors of 28: 1, 2, 4, 7, 14, 28 Factors of 15: 1, 3, 5, 15 The GCF is 1. The GCF is 3. Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 51: 1, 3, 17, 51 ANSWER ANSWER Because the GCF is 1, 28 and 45 are relatively prime. Because the GCF is 3, 15 and 51 are not relatively prime.