Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Math 81 Activity # 7 “Greatest Common Factor” Your Name: ___________________ Team Member #1__________________ Team Member #2.______________ Team Member #3__________________ Find the greatest common factor of 24 and 30. Method 1: List the factors of 24 and 30. Factors Factors 1 24 1 30 2 12 2 15 3 8 3 10 4 6 5 6 The common factors of 24 and 30 are 1, 2, 3, and 6. What is the greatest common factor? _____ Method 2: Using prime factorization and exponents. 24 2 12 3 4 2 2 Prime factorization is 2 2 2 3 30 3 10 2 5 Prime factorization is 2 3 5 The Fundamental Theorem of Arithmetic states that every integer greater than 1 is either prime or may be uniquely expressed as the product of prime numbers. We use this theorem to find the greatest common factor (GCF). 1) Use factor trees to find the unique prime factorization of each number (as seen above) 2) Then use exponential notation to represent the prime factorization. The prime factorization of 24 is 2 2 2 3 23 31 The prime factorization of 30 is 2 3 5 21 31 51 Observe we place the bases in ascending order (smallest to largest). 3) Write down all the bases they have in common only. 2 3 (we do not repeat the 2or 3) 4) Write down the smallest exponent per base 21 31 5) Multiply out the product 21 31 6 . Therefore, 6 is the greatest common factor (GCF) of 24 and 30. Method 3: Using prime factorization. Be careful this time, for the greatest common factor we circle the prime factors in common ONLY. 24: 2 30: 2 2 2 3 3 5 What prime numbers did you circle as a set? ______ Multiply this numbers, the product is ____. The Greatest common factor is ____. To remember this method for GCF try this G C F, circle all the common prime factors Problem 1: Find the greatest common factor of 24, 40, and 72. Find the prime factorization of each number 24, 40 and 72. 24 40 72 Prime factorization is Prime factorization is Prime factorization is _________. _________. _________. Insert all the prime numbers in the appropriate boxes for each number. Start by putting all the prime numbers for the largest number in this case 72. Then insert the rest of the numbers, notice the shaded boxes are there to guide you. Circle the prime numbers that are in common with all three numbers. 24: 40: 72: What is the GCF of 24, 40 and 72? _____ Problems: 1) Find the factors of 25. Factors 2) Find the factors of 26. Factors 3) Find the factors of 64. 4) Find the factors of 24. Factors Factors 5) Find the factors of 36. 6) Find the factors of 42. Factors Problems: Factors Use any method to find the GCF. 1) Find the GCF of 12 and 40. 2) Find the GCF of 14 and 18. 3) Find the GCF of 20 and 36. 4) Find the GCF of 15 and 35. 5) Find the GCF of 14, 18 and 36. 6) Find the GCF of 8, 16, 38. 7) Find the GCF of 120 and 144. 8) Find the GCF of 44 and 105.