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### Grade 6 - Mathematics1.35 GCF - Greatest Common Factor

 Greatest Common Factor (GCF) of two numbers is the largest number that divides both of the given numbers exactly. It is called their Greatest Common Divisor (G.C.D.) or Highest Common Factor (H.C.F.) or Greatest Common Factor (G.C.F). Method: Find the prime factors of the numbers Find the prime factors that are common to all of the numbers. Multiply the common prime factors The resulting number is the greatest common factor GCF Example: Find the GCF of 36, 48, and 60. Solution: Find the prime factors of these numbers: 36 = 2 x 2 x 3 x 3. 48 = 2 x 2 x 2 x 2 x 3. 60 = 2 x 2 x 3 x 5. Now, find the prime factors that are common to all of these three numbers. Here, 2, 2, and 3 are common prime factors. Multiply the common prime factors, 2 x 2 x 3 = 12. The resulting number (here, 12) is the greatest common factor of the given numbers. Directions: Answer the following questions. Also write at least 10 examples of your own.
 Q 1: Find the G.C.D. of 16, 30?2864 Q 2: What is the greatest number that divides 480, 450 and 210 exactly?50344030 Q 3: What is the greatest number which divides 370 and 514 leaving a remainder 10? (Hint: Subtract 10 from each number and then find their G.C.D.)74725652 Q 4: Find the G.C.D. of 45, 120?2051015 Q 5: Find the G.C.D. of 70, 210, 315?36354525 Q 6: What is the greatest number that divides 47, 67 and 107 leaving a remainder 7? (Hint: Subtract 7 form each number and then find their G.C.D.)20305040 Q 7: What is the greatest number which divides 690 and 875 leaving remainders 10 and 25 respectively?(Hint:- Subtract 10 from 690 and subtract 25 from 875 and then find G.C.D.)1758417076 Q 8: Find the G.C.D. of 60, 90, 150?30201040 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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