GCF of 27/20, 60/15, 98/99, 59/210
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 27/20, 60/15, 98/99, 59/210 i.e 1/13860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/20, 60/15, 98/99, 59/210.
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 27/20,60/15,98/99,59/210?
Given fractions are 27/20,60/15,98/99,59/210
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 27/20,60/15,98/99,59/210, numerators are 27,60,98,59
Denominators are 20,15,99,210
The GCF of 27,60,98,59 is 1 .
LCM of 20,15,99,210 is 13860.
The greatest common factor of 27/20,60/15,98/99,59/210 = [GCF of 27,60,98,59]/[LCM of 20,15,99,210]= 1/13860
Therefore, the GCF of 27/20,60/15,98/99,59/210 is 1/13860.
To find the highest common factor of 27,60,98,59, we have to find the factors of both numbers and list the highest common factor.
The factors of 27 are 1, 3, 9, 27
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 98 are 1, 2, 7, 14, 49, 98
The factors of 59 are 1, 59
The HCF of 27,60,98,59 is 1.
Lets's calculate GCF of 27,60,98,59
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 27,60,98,59 By Matching Biggest Common Factor Method
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 98
:1,2,7,14,49,98
Now, list down the factors of 59
:1,59
Greatest Common Factor
We found the factors 27,60,98,59 . The biggest common factor number is the GCF number.
So the greatest common factor 27,60,98,59 is 1.
Lets's calculate LCM of 20,15,99,210
| 2 | 20, 15, 99, 210 |
| 3 | 10, 15, 99, 105 |
| 5 | 10, 5, 33, 35 |
| 2, 1, 33, 7 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 2 x 1 x 33 x 7 = 13860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13860
Therefore, the GCF of Fractions 27/20,60/15,98/99,59/210 is 1/13860
Least Common Multiple of 20,15,99,210 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 20,15,99,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,15,99,210) = 1
common factors(in case of two or more numbers have common factors) = 450
GCF(20,15,99,210) x common factors =1 x 450 = 450
LCM(20,15,99,210) = ( 20 × 15 × 99 × 210 ) / 450
LCM(20,15,99,210) = 6237000 / 450
LCM(20,15,99,210) = 13860
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 27/20, 60/15, 98/99, 59/210
1. What is the HCF of 27,60,98,59?
The HCF of 27,60,98,59 is 1
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 27/20, 60/15, 98/99, 59/210?
Answer: GCF of Numerators as per given numbers 27/20, 60/15, 98/99, 59/210 is
GCF of Numerators i.e. for 27,60,98,59 is 1
LCM of denominators i.e. for 20,15,99,210 is 13860.
Thus, GCF of Fractions is 1/13860.Finally, GCF of Fractions for 27/20, 60/15, 98/99, 59/210 is 1/13860.