GCF of 82/237, 5314/5316
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 82/237, 5314/5316 i.e 2/419964 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/237, 5314/5316.
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 82/237,5314/5316?
Given fractions are 82/237,5314/5316
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 82/237,5314/5316, numerators are 82,5314
Denominators are 237,5316
The GCF of 82,5314 is 2 .
LCM of 237,5316 is 419964.
The greatest common factor of 82/237,5314/5316 = [GCF of 82,5314]/[LCM of 237,5316]= 2/419964
Therefore, the GCF of 82/237,5314/5316 is 2/419964.
To find the highest common factor of 82,5314, we have to find the factors of both numbers and list the highest common factor.
The factors of 82 are 1, 2, 41, 82
The factors of 5314 are 1, 2, 2657, 5314
The HCF of 82,5314 is 2.
Lets's calculate GCF of 82,5314
| 2 | 82, 5314 |
| 41, 2657 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 82,5314 By Matching Biggest Common Factor Method
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 5314
:1,2,2657,5314
Greatest Common Factor
We found the factors 82,5314 . The biggest common factor number is the GCF number.
So the greatest common factor 82,5314 is 2.
Lets's calculate LCM of 237,5316
| 3 | 237, 5316 |
| 79, 1772 |
∴ So the LCM of the given numbers is 3 x 79 x 1772 = 419964
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/419964
Therefore, the GCF of Fractions 82/237,5314/5316 is 2/419964
Least Common Multiple of 237,5316 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 237,5316 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(237,5316) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(237,5316) x common factors =3 x 1 = 3
LCM(237,5316) = ( 237 × 5316 ) / 3
LCM(237,5316) = 1259892 / 3
LCM(237,5316) = 419964
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FAQs on GCF of Fractions of 82/237, 5314/5316
1. What is the HCF of 82,5314?
The HCF of 82,5314 is 2
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 82/237, 5314/5316?
Answer: GCF of Numerators as per given numbers 82/237, 5314/5316 is
GCF of Numerators i.e. for 82,5314 is 2
LCM of denominators i.e. for 237,5316 is 419964.
Thus, GCF of Fractions is 2/419964.Finally, GCF of Fractions for 82/237, 5314/5316 is 2/419964.