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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Grade 6 - Mathematics
1.35 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:

  1. Find the prime factors of the numbers
  2. Find the prime factors that are common to all of the numbers.
  3. Multiply the common prime factors
  4. 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 70, 210, 315?
36
45
35
25

Q 2: Find the G.C.D. of 45, 120?
10
20
15
5

Q 3: 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.)
40
50
20
30

Q 4: Find the greatest number which divides 42 and 142 leaving remainder 2 in each case? (Hint: Subtract 2 from each number and then find their G.C.D.)
40
50
20
30

Q 5: Find the G.C.D. of 420, 630, 700?
60
70
40
50

Q 6: 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.)
170
76
175
84

Q 7: 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.)
56
74
52
72

Q 8: Find the G.C.D. of 60, 90, 150?
20
40
30
10

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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