Greatest Common factor Tool and Least Common Multiple Tool
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Being able to find the greatest common factor, or GCF, gives you an important tool to work with fractions in elementary school math. It is the first step in simplifying fractions. Simply put, a GCF is the largest number that divides evenly into multiple integers. Often you'll need to find the GCF of a numerator and denominator of a fraction so that you can divide each by the GCF and simplify the fraction.
Instructions
Read more: How to Find the Greatest Common Factor of Two Numbers | eHow http://www.ehow.com/how_4805007_common-factor-of-two-numbers.html#ixzz2Tu04TD6r
Instructions
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- 1 List the numbers whose GCF you're trying to find vertically on a piece of paper. For example, suppose you want to find the greatest common factor of 72 and 96.
- 2 Write the factors for your first number. Remember that factors are numbers that can go into the larger number evenly. It is sometimes easier to list factors by pairs. Then you can easily rearrange them in numerical order. For example, the multiples of 72 are 1 x 72, 2 x 36, 3 x 24, 4 x 18, 6 x 12 and 8 x 9. You can list these factors as follows:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- 3 Write out the multiples for the second number. In the example, you would write, "1 x 96, 2 x 48, 3 x 32, 4 x 24, 6 x 16 and 8 x 12." So in order, the factors would be:
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- 4 Compare the lists of factors. Find the largest factor that is in all of the lists. This is your greatest common factor. Concluding the example, the GCF would be 24 because that is the largest number in both lists.
- 1 List the numbers whose GCF you're trying to find vertically on a piece of paper. For example, suppose you want to find the greatest common factor of 72 and 96.
Read more: How to Find the Greatest Common Factor of Two Numbers | eHow http://www.ehow.com/how_4805007_common-factor-of-two-numbers.html#ixzz2Tu04TD6r
LCM (Least Common Multiple) and
GCF (Greatest Common Factor) To find either the Least Common Multiple (LCM) or Greatest Common Factor (GCF) of two numbers, you always start out the same way: you find the prime factorizations of the two numbers. Then you put the factors into a nice neat grid of rows and columns, and compare and contrast and take what you need.
For the GCF, you carry down only those factors that all the listings share; for the LCM, you carry down all the factors, regardless of how many or few values contained that factor in their listings.
http://www.purplemath.com/modules/lcm_gcf.htm
GCF (Greatest Common Factor) To find either the Least Common Multiple (LCM) or Greatest Common Factor (GCF) of two numbers, you always start out the same way: you find the prime factorizations of the two numbers. Then you put the factors into a nice neat grid of rows and columns, and compare and contrast and take what you need.
- Find the GCF and LCM of 2940 and 3150.
- First, I need to factor each value:
My prime factorizations are: Copyright © Elizabeth Stapel 2000-2011 All Rights Reserved
- 2940 = 2 × 2 × 3 × 5 × 7 × 7
3150 = 2 × 3 × 3 × 5 × 5 × 7
The Greatest Common Factor, the GCF, is the biggest number that will divide into (is a factor of) both 2940 and 3150. In other words, it's the number that contains all the factors common to both numbers. In this case, the GCF is the product of all the factors that 2940 and 3150 have in common.
Looking at the nice neat listing, I can see that the numbers both have a factor of 2; 2940 has a second copy of the factor 2, but 3150 does not, so I can only count the one copy toward my GCF. The numbers also share one copy of 3, one copy of 5, and one copy of 7.
On the other hand, the Least Common Multiple, the LCM, is the smallest number that both 2940 and 3150 will divide into. That is, it is the smallest number that contains both 2940 and 3150 as factors, the smallest number that is a multiple of both these values. Then it will be the smallest number that contains one of every factor in these two numbers.
Looking back at the listing, I see that 3150 has one copy of the factor of 2; 2940 has two copies. Since the LCM must contain all factors of each number, the LCM must contain both copies of 2. However, to avoid overduplication, the LCM does not need three copies, because neither 2940 nor 3150 contains three copies.
- So, my LCM of 2940 and 3150 must contain both copies of the factor 2. By the same reasoning, the LCM must contain both copies of 3, both copies of 5, and both copies of 7:
For the GCF, you carry down only those factors that all the listings share; for the LCM, you carry down all the factors, regardless of how many or few values contained that factor in their listings.
- Find the LCM and GCF of 27, 90, and 84.
- First, I need to find the prime factorizations:
- Find the GCF and LCM of 3, 6, and 8.
- First I factor the numbers and list their prime factorizations:
- Then the GCF is 1 and the LCM is 2 × 2 × 2 × 3 = 24.
- Find the LCM of x3 + 5x2 + 6x and 2x3 + 4x2.
- First I factor the polynomials: x3 + 5x2 + 6x = x(x2 + 5x + 6) = x(x + 2)(x + 3), and 2x3 + 4x2 = 2x2(x + 2). Then I list these factors out, nice and neat:
- The LCM is 2x2(x + 2)(x + 3).
http://www.purplemath.com/modules/lcm_gcf.htm