Basic Mathematics

The Greatest Common Factor (GCF)

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The Greatest Common Factor (GCF)
Greatest Common Factor - The greatest common factor of two or more numbers is the greatest number that is a factor of each of them.
The abbreviation for the greatest common factor is GCF.
Find the GCF of 8 and 12.
The factors of 8 are 1, 2, 4 and 8.
The factors of 12 are 1,2,3,4,6, and 12.
The largest factor that appears in both sets of factors is 4.
The greatest common factor (GCF) of 8 and 12 is 4.
The Greatest Common Factor (GCF)
Another way to think about the greatest common factor (GCF) is as the largest whole number that divides evenly into all of the numbers.
The GCF of 6 and 15 is 3.
The GCF of 6 and 12 is 6.
The GCF of 6 and 5 is 1.
The GCF of 12, 18, and 24 is 6.
The GCF of 16, 24, 32, and 64 is 8.
The Greatest Common Factor (GCF)
One method of finding the GCF of two or more numbers is to find the prime factorization of each.
    Find the GCF of 36 and 60.

  1. Factor both the numbers into their prime factors.
    36 = 2 × 2 × 3 × 3
    60 = 2 × 2 × 3 × 5
  2. Match the common factors between the two (or more) prime factorizations.
    3. 36 = 2 × 2 × 3 × 3
    60 = 2 × 2 × 3 × 5
    2 appears twice (2 × 2), and 3 appears once.

  3. Multiply these common factors together to get the GCF.
    4. GCF = 2 × 2 × 3 = 12
The Greatest Common Factor (GCF)
Another method of finding the GCF of two or more numbers is to find all the factors of the smallest number. The largest of these that divides the other numbers is the GCF.

Find the GCF of 12, 15, and 6.

The factors of 6 (the smallest) are 1, 2, 3, and 6.

   1 divides 12 and 15
   2 doesn't divide 15
   3 divides 12 and 15
   6 doesn't divide 15

3 is the largest factor of 6 that also divides 12 and 15. GCF = 3
The Greatest Common Factor (GCF)
Click on the greatest common factor (GCF) of these numbers.
10, 20
    5
  10
200
  20
None of these
Question 1 of 8
5 is a common factor, but it's not the greatest common factor. Try again.
The largest number that is a factor of both 10 and 20 is 10.
200 is a multiple of 10 and 20. It's not a factor. Try again.
20 is not a factor of 10. Try again.
One of these is the GCF of 10 and 20. Try again.
The greatest common factor (GCF) is the largest number that divides 10 and 20 evenly.
The Greatest Common Factor (GCF)
Click on the greatest common factor (GCF) of these numbers.
12, 18
24
36
  3
  6
None of these
Question 2 of 8
24 is not a factor of either 12 or 18. Try again.
36 is a multiple of 12 and 18. It is not a factor. Try again.
3 is a common factor, but it's not the greatest common factor. Try again.
The largest number that is a factor of both 12 and 18 is 6.
One of these is the GCF of 12 and 18. Try again.
The greatest common factor (GCF) is the largest number that divides 12 and 18 evenly.
The Greatest Common Factor (GCF)
Click on the greatest common factor (GCF) of the numerator and denominator.
\[\frac{10}{15}\]
  5
20
30
10
None of these
Question 3 of 8
The largest number that is a factor of both 10 and 15 is 5.
20 is not a factor of either 10 or 15. Try again.
30 is a multiple of 10 and 15. It is not a factor. Try again.
10 is not a factor of 15. Try again.
One of these is the GCF of 10 and 15. Try again.
The greatest common factor (GCF) is the largest number that divides 10 and 15 evenly.
The Greatest Common Factor (GCF)
Click on the greatest common factor (GCF) of these numbers.
16, 40
  2
16
  4
80
None of these
Question 4 of 8
2 is a common factor, but it's not the greatest common factor. Try again.
16 is not a factor of 40. Try again.
4 is a common factor, but it's not the greatest common factor. Try again.
80 is a multiple of 16 and 40. It is not a factor. Try again.
The largest number that is a factor of both 16 and 40 is 8.
The greatest common factor (GCF) is the largest number that divides 16 and 40 evenly.
The Greatest Common Factor (GCF)
Click on the greatest common factor (GCF) of the numerator and denominator.
\[\frac{18}{15}\]
18
  9
  3
  6
None of these
Question 5 of 8
18 is not a factor of 45. Try again.
The largest number that is a factor of both 18 and 45 is 9.
3 is a common factor, but it's not the greatest common factor. Try again.
6 is not a factor of 45. Try again.
One of these is the GCF of 18 and 45. Try again.
The greatest common factor (GCF) is the largest number that divides 18 and 45 evenly.
The Greatest Common Factor (GCF)
Click on the greatest common factor (GCF) of these numbers.
18, 24, 36
  9
  3
18
  6
None of these
Question 6 of 8
9 is not a factor of 24. Try again.
3 is a common factor of these numbers, but it's not the greatest common factor. Try again.
18 is not a factor of 24. Try again.
The largest number that is a factor of 18, 24, and 36 is 6.
One of these is the GCF of 18, 24, and 36. Try again.
The greatest common factor (GCF) is the largest number that divides 18, 24, and 36 evenly.
The Greatest Common Factor (GCF)
Click on the greatest common factor (GCF) of these numbers.
4, 6, 15
0
3
2
1
None of these
Question 7 of 8
0 is not a factor of any of these numbers. Try again.
3 is not a factor of 4. Try again.
2 is not a factor of 15. Try again.
The only number that is a factor of all of these is 1.
One of these is the GCF of 4, 6, and 15. Try again.
The greatest common factor (GCF) is the largest number that divides 4, 6, and 15 evenly.
The Greatest Common Factor (GCF)
Click on the greatest common factor (GCF) of these numbers.
60, 144
  4
12
  2
24
None of these
Question 8 of 8
4 is a common factor, but it's not the greatest common factor. Try again.
The largest number that is a factor of both 60 and 144 is 12.
2 is a common factor, but it's not the greatest common factor. Try again.
24 is not a factor of 60. Try again.
One of these is the GCF of 60 and 144 Try again.
The greatest common factor (GCF) is the largest number that divides 60 and 144 evenly.
The Greatest Common Factor (GCF)