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Transparency 1. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 1-4b. Objective. Find the prime factorization of a composite number. Example 1-4b. Vocabulary. Prime number.

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  1. Transparency 1 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 1-4b Objective Find the prime factorization of a composite number

  4. Example 1-4b Vocabulary Prime number A whole number greater than 1 that has exactly two factors, 1 and itself

  5. Example 1-4b Vocabulary Composite number A whole number greater than 1 that has more than 2 factors

  6. Example 1-4b Vocabulary Prime factorization Expressing a composite number as a product of prime numbers

  7. Example 1-4b Vocabulary Factor tree A diagram showing the prime factorization of a number

  8. Example 1-4b Review Vocabulary Factors Two or more numbers that are multiplied together to form a product

  9. Lesson 1 Contents Example 1Identify Numbers as Prime or Composite Example 2Identify Numbers as Prime or Composite Example 3Find the Prime Factorization Example 4Factor an Algebraic Expression

  10. Example 1-1a Determine whether the number 63 is prime or composite. Write the number 63 All numbers (except 1) has 2 factors: 1 and the number itself 6 + 3 = 9 Determine if any number other than 1 and 63 are factors of 63 9  3 = 3 Remember divisibility rules: If the sum of the digits is divisible by 3 then the number is divisible by 3 63 is divisible by 3 so is not prime Answer: Composite 1/4

  11. Example 1-1b Determine whether the number 41 is prime or composite. Answer:prime 1/4

  12. Example 1-2a Determine whether the number 29 is prime or composite. Write the number 29 All numbers (except 1) has 2 factors: 1 and the number itself 2 + 9 = 11 Determine if any number other than 1 and 29 are factors of 29 Remember divisibility rules: If the sum of the digits is divisible by 3 then the number is divisible by 3 2/4

  13. Example 1-2a Determine whether the number 29 is prime or composite. Remember divisibility rules: 29 11 is not divisible by 3 so 29 is not divisible by 3 2 + 9 = 11 29 is not even so is not divisible by 2 Continue checking divisibility by prime numbers The one’s digit is not a 0 or 5 so is not divisible by 5 2/4

  14. Example 1-2a Determine whether the number 29 is prime or composite. Remember divisibility rules: 29 29 is not divisible by 7 because 7  4 = 28 2 + 9 = 11 29 is not divisible by 11 because 11  3 = 33 Since we have checked divisibility past 29 we have confirmed that 29 is a prime number Answer: Prime 2/4

  15. Example 1-2b Determine whether the number 24 is prime or composite. Answer:composite 2/4

  16. Example 1-3a Find the prime factorization of 100. Write number then use factorization ladder Decide on prime number that will go evenly into 100 2 100 50 2 Can use any prime factor like 2 or 5 5 25 5 Decide on prime number that will go evenly into 50 Decide on prime number that will go evenly into 25 5 is a prime number so you are done prime factoring 3/4

  17. Example 1-3a Find the prime factorization of 100. Write using prime numbers and exponents 2 100 Write the smallest prime number that was used 2 50 2 5 25 Circle the 2’s that were used 5 2 two’s were used so that is the exponent with the 2  Put the multiplication sign 2 2 3/4

  18. Example 1-3a Find the prime factorization of 100. Write the next smallest prime number which is 5 2 100 Circle the 5’s that were used 50 2 2 five's were used so that is the exponent with the 2 5 25 5 All prime numbers used have been circled so you are done!  2 5 2 2 Answer:22 52 3/4

  19. Example 1-3b Find the prime factorization of 72. Answer: 23 32 3/4

  20. ALGEBRA Factor Example 1-4a Write number then use factorization ladder Decide on prime number that will go evenly into 21 3 21m2n 7m2n 7 7 The prime number 3 will divide into 21 evenly Divide 21 by 3 Bring down m2n Decide on prime number that will go evenly into 7 The prime number 7 will divide into 7 evenly 4/4

  21. ALGEBRA Factor Example 1-4a Divide 7 into 7 then use the Identity Property to multiply 1  m2n 3 21m2n Since m2 = m  m, m can be a prime variable 7m2n 7 7 m m2n Divide m into m2 which will be m m mn m Bring down the n Remember a variable by itself is prime so use m as a prime 4/4

  22. ALGEBRA Factor Example 1-4a Divide m into mn which will leave n 3 21m2n 7m2n 7 7 The variable is a prime and is by itself so you are done prime factoring! m m2n m mn m n Now write the answer as factors 4/4

  23. ALGEBRA Factor Example 1-4a Write the smallest prime number which is 3 3 21m2n 7m2n Circle the 3 7 7 m m2n Since the direction say “factor” then do not use exponents m mn m n Put the multiplication sign Circle the next factor which is 7 and write it down 3 3  3  7  Put the multiplication sign 4/4

  24. ALGEBRA Factor Example 1-4a Circle the next factor which is m and write it down 3 21m2n 7m2n 7 7 Put the multiplication sign m m2n Circle the next factor which is m and write it down m mn m n Put the multiplication sign Answer: Circle the next factor which is n and write it down 3  7  m m  m  m m  m  m  m  n 4/4

  25. ALGEBRA Factor Answer: Example 1-4b * 4/4

  26. End of Lesson 1 Assignment

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