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Greatest Common Factor

Greatest Common Factor. GCF. Divisibility Rules. 2 , if it ends in a even number in the ones place ( 0,2,4,6,8 ). Example: 55 8 because there is a 8 in the ones place 3 , if the sum of its digits is divisible by 3. Example: 81 because 8 + 1 = 9 and 9 is divisible by 3

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Greatest Common Factor

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  1. Greatest Common Factor GCF

  2. Divisibility Rules • 2, if it ends in a even number in the ones place (0,2,4,6,8). • Example: 558because there is a 8 in the ones place • 3, if the sum of its digits is divisible by 3. • Example: 81because 8 + 1 = 9 and 9 is divisible by 3 • 4, if the last 2 digits are divisible by 4 • Example: 124because 24 is divisible by 4 • 5, if the ones digit is 5 or 0. • Example: 1125because there is a 5 in the ones place

  3. Divisibility Rules • 6, if the number is divisible by both 2 and 3 • Example: 48 • There is an 8 in the ones place so it is divisible by 2 • 8 + 4 = 12 and 12 is divisible by 3 • 8, if the last 3 digits are divisible by 8 • Example: 1240because 240 is divisible by 8 • 9, if the sum of the digits is divisible by 9 • Example: 468because 4 + 6 + 8 = 18 and 18 is divisible by 9 • 10, if the number ends in a zero • Example: 50because the number ends in zero

  4. Common Factors • DEFINITION: Any integer that can evenly divide into all the numbers in a given set of numbers • Example: Find the common factors of 10 and 20 by listing all the factors. • Factors of 10: _____________________________ • Factors of 20: _____________________________ • Common Factors of 10 and 20: ______________________ 1, 2, 5, 10 1, 2, 4, 5, 10, 20 1, 2, 5, 10

  5. Greatest Common Factor • DEFINITION: The largest integer that can evenly divide into all of the numbers in a set of numbers. • There are two methods we can use to find the greatest common factor of two or more numbers… • METHOD 1: MAKE A LIST • List all the factors of each number. Circle the greatest factor that appears in the lists.

  6. Greatest Common Factor METHOD 1: MAKE A LIST List all the factors of each number. Circle the greatest factor that appears in the lists. Example 1: Find the greatest common factor of 12 and 18 Factors of 12: _____________________________ Factors of 18: _____________________________ Greatest Common Factor of 12 and 18: __ 1, 2, 3, 4, 6, 12 1, 2, 3, 6, 9, 18 6

  7. Greatest Common Factor METHOD 1: MAKE A LIST List all the factors of each number. Circle the greatest factor that appears in the lists. Example 2: Find the greatest common factor of 12, 18, and 24 Factors of 12: _____________________________ Factors of 18: _____________________________ Factors of 24: _____________________________ Greatest Common Factor of 12, 18, and 24: __ 1, 2, 3, 4, 6, 12 1, 2, 3, 6, 9, 18 1, 2, 3, 4, 6, 8, 12, 24 6

  8. Greatest Common Factor METHOD 2: Upside Down Cake Example 1: Find the GCF(12,32) Greatest Common Factor of 12 and 32: __ If you are “stuck” always start with 2 2 12 32 6 16 2 Since 3 and 8 share no common factors, stop here! 3 8 Multiply the circled numbers 4

  9. Greatest Common Factor METHOD 2: Upside Down Cake Example 1: Find the GCF(32,96) Greatest Common Factor of 12 and 32: ___ If you are “stuck” always start with 2 2 32 96 16 48 2 2 8 24 4 12 2 2 6 2 Since one of your numbers is now 1, stop here! 1 3 32

  10. Greatest Common Factor METHOD 2: Upside Down Cake Example 2: Find the GCF(30,48,120) Greatest Common Factor of 30,48,120: ___ If you are “stuck” always start with 2 2 30 48 120 If 2 doesn’t work, go on to the next number 15 24 60 3 Since your numbers share no common factors, stop here! 5 8 20 6

  11. Mr. Grover wants to make shelves for his garage using an 18-foot board and a 36-foot board. He will cut the boards to make shelves of the same length and wants to use all of both boards. Find the greatest possible length of each shelf. Answer 18 foot boards

  12. The SGB reps are making spirit ribbons. Blue ribbon comes in a 24 inch spool, red ribbon comes in a 30 inch spool, and gold ribbon comes in a 36 inch spool. The SGB reps want to cut strips of equal length, using the entire spool of each ribbon. What is the length of greatest piece of ribbon that can be cut from each spool? Answer 6 inches

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