GCF of 7281/198, 5457/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7281/198, 5457/214 i.e 3/21186 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7281/198, 5457/214.
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 7281/198,5457/214?
Given fractions are 7281/198,5457/214
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 7281/198,5457/214, numerators are 7281,5457
Denominators are 198,214
The GCF of 7281,5457 is 3 .
LCM of 198,214 is 21186.
The greatest common factor of 7281/198,5457/214 = [GCF of 7281,5457]/[LCM of 198,214]= 3/21186
Therefore, the GCF of 7281/198,5457/214 is 3/21186.
To find the highest common factor of 7281,5457, we have to find the factors of both numbers and list the highest common factor.
The factors of 7281 are 1, 3, 9, 809, 2427, 7281
The factors of 5457 are 1, 3, 17, 51, 107, 321, 1819, 5457
The HCF of 7281,5457 is 3.
Lets's calculate GCF of 7281,5457
| 3 | 7281, 5457 |
| 2427, 1819 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7281,5457 By Matching Biggest Common Factor Method
Now, list down the factors of 7281
:1,3,9,809,2427,7281
Now, list down the factors of 5457
:1,3,17,51,107,321,1819,5457
Greatest Common Factor
We found the factors 7281,5457 . The biggest common factor number is the GCF number.
So the greatest common factor 7281,5457 is 3.
Lets's calculate LCM of 198,214
| 2 | 198, 214 |
| 99, 107 |
∴ So the LCM of the given numbers is 2 x 99 x 107 = 21186
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/21186
Therefore, the GCF of Fractions 7281/198,5457/214 is 3/21186
Least Common Multiple of 198,214 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 198,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(198,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(198,214) x common factors =2 x 1 = 2
LCM(198,214) = ( 198 × 214 ) / 2
LCM(198,214) = 42372 / 2
LCM(198,214) = 21186
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FAQs on GCF of Fractions of 7281/198, 5457/214
1. What is the HCF of 7281,5457?
The HCF of 7281,5457 is 3
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 7281/198, 5457/214?
Answer: GCF of Numerators as per given numbers 7281/198, 5457/214 is
GCF of Numerators i.e. for 7281,5457 is 3
LCM of denominators i.e. for 198,214 is 21186.
Thus, GCF of Fractions is 3/21186.Finally, GCF of Fractions for 7281/198, 5457/214 is 3/21186.