GCF of 131/51, 538/684
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 131/51, 538/684 i.e 1/11628 easily. The following is the detailed procedure to determine the greatest common factor of fractions 131/51, 538/684.
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 131/51,538/684?
Given fractions are 131/51,538/684
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 131/51,538/684, numerators are 131,538
Denominators are 51,684
The GCF of 131,538 is 1 .
LCM of 51,684 is 11628.
The greatest common factor of 131/51,538/684 = [GCF of 131,538]/[LCM of 51,684]= 1/11628
Therefore, the GCF of 131/51,538/684 is 1/11628.
To find the highest common factor of 131,538, we have to find the factors of both numbers and list the highest common factor.
The factors of 131 are 1, 131
The factors of 538 are 1, 2, 269, 538
The HCF of 131,538 is 1.
Lets's calculate GCF of 131,538
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 131,538 By Matching Biggest Common Factor Method
Now, list down the factors of 131
:1,131
Now, list down the factors of 538
:1,2,269,538
Greatest Common Factor
We found the factors 131,538 . The biggest common factor number is the GCF number.
So the greatest common factor 131,538 is 1.
Lets's calculate LCM of 51,684
| 3 | 51, 684 |
| 17, 228 |
∴ So the LCM of the given numbers is 3 x 17 x 228 = 11628
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11628
Therefore, the GCF of Fractions 131/51,538/684 is 1/11628
Least Common Multiple of 51,684 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 51,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,684) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(51,684) x common factors =3 x 1 = 3
LCM(51,684) = ( 51 × 684 ) / 3
LCM(51,684) = 34884 / 3
LCM(51,684) = 11628
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FAQs on GCF of Fractions of 131/51, 538/684
1. What is the HCF of 131,538?
The HCF of 131,538 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 131/51, 538/684?
Answer: GCF of Numerators as per given numbers 131/51, 538/684 is
GCF of Numerators i.e. for 131,538 is 1
LCM of denominators i.e. for 51,684 is 11628.
Thus, GCF of Fractions is 1/11628.Finally, GCF of Fractions for 131/51, 538/684 is 1/11628.