GCF of 516/418, 138/878
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 516/418, 138/878 i.e 6/183502 easily. The following is the detailed procedure to determine the greatest common factor of fractions 516/418, 138/878.
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 516/418,138/878?
Given fractions are 516/418,138/878
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 516/418,138/878, numerators are 516,138
Denominators are 418,878
The GCF of 516,138 is 6 .
LCM of 418,878 is 183502.
The greatest common factor of 516/418,138/878 = [GCF of 516,138]/[LCM of 418,878]= 6/183502
Therefore, the GCF of 516/418,138/878 is 6/183502.
To find the highest common factor of 516,138, we have to find the factors of both numbers and list the highest common factor.
The factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The HCF of 516,138 is 6.
Lets's calculate GCF of 516,138
| 2 | 516, 138 |
| 3 | 258, 69 |
| 86, 23 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 516,138 By Matching Biggest Common Factor Method
Now, list down the factors of 516
:1,2,3,4,6,12,43,86,129,172,258,516
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 516,138 . The biggest common factor number is the GCF number.
So the greatest common factor 516,138 is 6.
Lets's calculate LCM of 418,878
| 2 | 418, 878 |
| 209, 439 |
∴ So the LCM of the given numbers is 2 x 209 x 439 = 183502
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/183502
Therefore, the GCF of Fractions 516/418,138/878 is 6/183502
Least Common Multiple of 418,878 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 418,878 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(418,878) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(418,878) x common factors =2 x 1 = 2
LCM(418,878) = ( 418 × 878 ) / 2
LCM(418,878) = 367004 / 2
LCM(418,878) = 183502
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FAQs on GCF of Fractions of 516/418, 138/878
1. What is the HCF of 516,138?
The HCF of 516,138 is 6
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 516/418, 138/878?
Answer: GCF of Numerators as per given numbers 516/418, 138/878 is
GCF of Numerators i.e. for 516,138 is 6
LCM of denominators i.e. for 418,878 is 183502.
Thus, GCF of Fractions is 6/183502.Finally, GCF of Fractions for 516/418, 138/878 is 6/183502.