Objectives Vocabulary Example 1 Example 2 Example 3
Objectives Vocabulary Example 1 Example 2 Example 3 Quick Quiz
• Identify all the factors of a given number • To understand distinguish prime and composite numbers • To find prime factorizations • To identify multiples • To find common and GCFs, and common and LCMs • To see how factors and multiples are related
• factor pair • greatest common factor, GCF • composite number • relatively prime • prime factorization • common multiple • prime number • multiple • common factor • least common multiple (LCM)
A. Determine whether 31 is prime or composite. Find factors of 31 by listing the whole number pairs whose product is 31. 31 = 1 × 31 The number 31 has only two factors. Answer: Therefore, 31 is a prime number.
B. Determine whether 36 is prime or composite. Find factors of 36 by listing the whole number pairs whose product is 36. 36 = 1 × 36 36 = 2 × 18 36 = 3 × 12 36 = 4 × 9 36 = 6 × 6 The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Answer: Since the number has more than two factors, it is composite.
A. Determine whether 49 is prime or composite. A. prime B. composite C. neither D. prime and composite 1. 2. 3. 4. A B C D
B. Determine whether 29 is prime or composite. A. prime B. composite C. neither D. prime and composite 1. 2. 3. 4. A B C D
A. Find the GCF of 16 and 24. Method 1 List the factors of 16: 1, 2, 4, 8, 16 factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 The common factors are 1, 2, 4, and 8. The greatest common factor is 8.
Method 2 Use prime factorization. 16: 2 ● 2 ● 2 24: 2 ● 2 ● 3 Common factors of 16 and 24: 2, 2, 2 The GCF is the product of the common prime factors. 2● 2● 2=8 Answer: The GCF of 16 and 24 is 8. Greatest Common Factor
B. Find the GCF of 28 and 35. First, factor each number completely. Then circle the common factors. 28: 2 ● 7 35: 5● 7 The common prime factor is 7. Answer: The GCF of 28 and 35 is 7.
C. Find the GCF of 12, 48, and 72. 12: 2 ● 3 48: 2 ● 2 ● 3 72: 2 ● 2 ● 3 The common prime factors are 2, 2, and 3. Answer: The GCF of 12, 48, and 72 is 2 ● 3 or 12.
A. Find the GCF of 18 and 30. A. 3 B. 6 C. 2 D. 9 1. 2. 3. 4. A B C D
B. Find the GCF of 24 and 32. A. 2 B. 6 C. 8 D. 12 1. 2. 3. 4. A B C D
C. Find the GCF of 30, 42, and 60. A. 6 B. 3 C. 12 D. 2 1. 2. 3. 4. A B C D
Find the LCM of 168 and 180. Number 168 180 Prime Factorization Exponential Form 2● 2● 2● 3● 7 23 ● 7 2● 2● 3● 3● 5 22 ● 32 ● 5 The prime factors of both numbers are 2, 3, 5, and 7. Multiply the greatest power of 2, 3, 5, and 7 appearing in either factorization. LCM = 23 ● 32 ● 5 ● 7 = 2520 Answer: The LCM of 168 and 180 is 2520.
Find the LCM of 144 and 96. A. 24 B. 144 C. 288 D. 13, 824 1. 2. 3. 4. A B C D
Select a different connection that will give the same output as a × 36 machine. A. × 6 and × 30 B. × 14 and × 22 C. × 2 and × 20 D. × 4 and × 9 1. 2. 3. 4. A B C D
Select a different connection that will give the same output as a × 24 machine. A. × 3 and × 8 B. × 20 and × 4 C. × 6 and × 5 D. × 12 and × 12 1. 2. 3. 4. A B C D
Select a different connection that will give the same output as a × 100 machine. A. × 30 and × 70 B. × 50 and × 50 C. × 5 and × 20 D. × 1 and × 10 1. 2. 3. 4. A B C D
Which of the following numbers are not factors of 18? 8, 9, 2, 4, 12, 36, 3 A. 4, 12, 36 B. 8, 4, 12, 36 C. 9, 4, 12, 3 D. 8, 4, 12, 3 1. 2. 3. 4. A B C D
A. Find the greatest common factor for 24 and 56. A. relatively prime B. 6 C. 8 D. 12 1. 2. 3. 4. A B C D
B. Find the greatest common factor for 15 and 23. A. relatively prime B. 5 C. 3 D. 15 1. 2. 3. 4. A B C D
C. Find the greatest common factor for 8 and 15. A. 4 B. relatively prime C. 8 D. 2 1. 2. 3. 4. A B C D
What are the first five multiples of 7? A. 7, 49, 343, 2401, 16807 B. 7, 35, 175, 875, 4375 C. 7, 12, 17, 22, 27 D. 7, 14, 21, 28, 35 1. 2. 3. 4. A B C D
Image Bank Math Tools Multilingual e-Glossary Greatest Common Factor
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