Prime Factorization. In my own words
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- Carol Gilbert
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1 Warm- up Problem What is a prime number? A PRIME number is an INTEGER greater than 1 with EXACTLY 2 positive factors, 1 and the number ITSELF. Examples of prime numbers: 2, 3, 5, 7 What is a composite number? A COMPOSITE number is an INTEGER greater than 1 with MORE than 2 positive FACTORS. Examples of composite numbers: 4, 6, 8, 9, 10 What about ONE? Practice: Prime or Composite? Convince me! What is prime factorization? Factor Trees The number 1 is NEITHER prime nor composite. 1) 23 prime; factors are only 1, 23 2) 129 composite; factors include 3 Prime FACTORIZATION means finding which PRIME numbers multiply together to make the ORIGINAL number. Factor TREES are useful to find a number s PRIME FACTORIZATION ! 11
2 Practice: Use a factor tree to write the prime factorization of each number. 3) 72 2! 3! 4) ! 5) Find the prime factors and variable factors of 12a! b! c 3 2! a b c What is Greatest Common Factor (GCF)? Method 1: List factors Method 2: Prime Factorization for finding GCF COMMON FACTORS are factors that are the same for two or more numbers. Find the common factors of 18 and 4: Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 4: 1, 2, 4 GREATEST COMMON FACTOR (GCF) is the largest factor that both numbers have in common! Find the GCF of 18 and 4: 2 You can use PRIME factorization to find the GCF. Factor trees: Find the GCF of 40 and 60. Prime factorizations: 40:2! 5 60:2! 3 5
3 Circle the GREATEST prime factors that BOTH numbers have in common. 2! 5 Multiply those together to find the GCF! GCF of 40 and 60: 20 Steps Practice with numerical and variable expressions: Find the GCF using prime factorization. To find GCF using Prime Factorization: STEP 1: Make factor TREES. STEP 2: Write PRIME factorizations. STEP 3: List GREATEST prime common factors. STEP 4: MULTIPLY the greatest prime common factors together. 6) 8 and ) 12 and ) 6a! b and 4a! b 2a! b 9) 12r! and 8r 4r 10) 15m! n and 45m 15m
4 Warm- up Problem What is a prime number? A number is an greater than 1 with 2 positive factors, 1 and the number. Examples of prime numbers: What is a composite number? A number is an greater than 1 with than 2 positive. Examples of composite numbers: What about ONE? Practice: Prime or Composite? Convince me! What is prime factorization? Factor Trees The number 1 is prime nor composite. 1) 23 2) 129 Prime means finding which numbers multiply together to make the number. Factor are useful to find a number s. 825
5 Practice: Use a factor tree to write the prime factorization of each number. 3) 72 4) 121 5) Find the prime factors and variable factors of 12a! b! c What is Greatest Common Factor (GCF)? Method 1: List factors are factors that are the same for two or more numbers. Find the common factors of 18 and 4: Factors of 18: Factors of 4: (GCF) is the largest factor that both numbers have in common! Find the GCF of 18 and 4: Method 2: Prime Factorization for finding GCF You can use factorization to find the GCF. Find the GCF of 40 and 60. Factor trees: Prime factorizations: 40: 60:
6 Circle the prime factors that numbers have in common. Multiply those together to find the GCF! GCF of 40 and 60: Steps Practice with numerical and variable expressions: Find the GCF using prime factorization. To find GCF using Prime Factorization: STEP 1: Make factor. STEP 2: Write factorizations. STEP 3: List prime common factors. STEP 4: the greatest prime common factors together. 6) 8 and 20 7) 12 and 87 8) 6a! b and 4a! b 9) 12r! and 8r 10) 15m! n and 45m
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