GCF of 20/21, 30/28, 720/286
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 20/21, 30/28, 720/286 i.e 10/12012 easily. The following is the detailed procedure to determine the greatest common factor of fractions 20/21, 30/28, 720/286.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 20/21,30/28,720/286?
Given fractions are 20/21,30/28,720/286
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 20/21,30/28,720/286, numerators are 20,30,720
Denominators are 21,28,286
The GCF of 20,30,720 is 10 .
LCM of 21,28,286 is 12012.
The greatest common factor of 20/21,30/28,720/286 = [GCF of 20,30,720]/[LCM of 21,28,286]= 10/12012
Therefore, the GCF of 20/21,30/28,720/286 is 10/12012.
To find the highest common factor of 20,30,720, we have to find the factors of both numbers and list the highest common factor.
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
The HCF of 20,30,720 is 10.
Lets's calculate GCF of 20,30,720
| 2 | 20, 30, 720 |
| 5 | 10, 15, 360 |
| 2, 3, 72 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 20,30,720 By Matching Biggest Common Factor Method
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 720
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360,720
Greatest Common Factor
We found the factors 20,30,720 . The biggest common factor number is the GCF number.
So the greatest common factor 20,30,720 is 10.
Lets's calculate LCM of 21,28,286
| 2 | 21, 28, 286 |
| 7 | 21, 14, 143 |
| 3, 2, 143 |
∴ So the LCM of the given numbers is 2 x 7 x 3 x 2 x 143 = 12012
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/12012
Therefore, the GCF of Fractions 20/21,30/28,720/286 is 10/12012
Least Common Multiple of 21,28,286 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 21,28,286 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,28,286) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(21,28,286) x common factors =1 x 14 = 14
LCM(21,28,286) = ( 21 × 28 × 286 ) / 14
LCM(21,28,286) = 168168 / 14
LCM(21,28,286) = 12012
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FAQs on GCF of Fractions of 20/21, 30/28, 720/286
1. What is the HCF of 20,30,720?
The HCF of 20,30,720 is 10
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 20/21, 30/28, 720/286?
Answer: GCF of Numerators as per given numbers 20/21, 30/28, 720/286 is
GCF of Numerators i.e. for 20,30,720 is 10
LCM of denominators i.e. for 21,28,286 is 12012.
Thus, GCF of Fractions is 10/12012.Finally, GCF of Fractions for 20/21, 30/28, 720/286 is 10/12012.