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

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

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

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

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

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

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

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 Example 1-1a

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

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 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 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 Example 1-2a

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

Find the prime factorization of 100. Write number then use factorization ladder Decide on prime number that will go evenly into 100 2 100 2 50 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 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 2 50 5 25 Circle the 2’s that were used 5 2 two’s were used so that is the exponent with the 2 2  2 Put the multiplication sign 3/4 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 2 50 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  2 5 2 Answer: 22  52 3/4 Example 1-3a

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

Write number then use factorization ladder ALGEBRA Factor Write number then use factorization ladder 3 21m2n Decide on prime number that will go evenly into 21 7 7m2n 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 Example 1-4a

Divide 7 into 7 then use the Identity Property to multiply 1  m2n ALGEBRA Factor 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 7 7m2n 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 Example 1-4a

Divide m into mn which will leave n 3 21m2n 7 7m2n 7 ALGEBRA Factor Divide m into mn which will leave n 3 21m2n 7 7m2n 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 Example 1-4a

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

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

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

Assignment Lesson 5:1 Prime Factorization 13 - 35 All End of Lesson 1