GCF of 334/78, 777/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 334/78, 777/414 i.e 1/5382 easily. The following is the detailed procedure to determine the greatest common factor of fractions 334/78, 777/414.
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 334/78,777/414?
Given fractions are 334/78,777/414
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 334/78,777/414, numerators are 334,777
Denominators are 78,414
The GCF of 334,777 is 1 .
LCM of 78,414 is 5382.
The greatest common factor of 334/78,777/414 = [GCF of 334,777]/[LCM of 78,414]= 1/5382
Therefore, the GCF of 334/78,777/414 is 1/5382.
To find the highest common factor of 334,777, we have to find the factors of both numbers and list the highest common factor.
The factors of 334 are 1, 2, 167, 334
The factors of 777 are 1, 3, 7, 21, 37, 111, 259, 777
The HCF of 334,777 is 1.
Lets's calculate GCF of 334,777
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 334,777 By Matching Biggest Common Factor Method
Now, list down the factors of 334
:1,2,167,334
Now, list down the factors of 777
:1,3,7,21,37,111,259,777
Greatest Common Factor
We found the factors 334,777 . The biggest common factor number is the GCF number.
So the greatest common factor 334,777 is 1.
Lets's calculate LCM of 78,414
| 2 | 78, 414 |
| 3 | 39, 207 |
| 13, 69 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 69 = 5382
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5382
Therefore, the GCF of Fractions 334/78,777/414 is 1/5382
Least Common Multiple of 78,414 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 78,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,414) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(78,414) x common factors =6 x 1 = 6
LCM(78,414) = ( 78 × 414 ) / 6
LCM(78,414) = 32292 / 6
LCM(78,414) = 5382
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FAQs on GCF of Fractions of 334/78, 777/414
1. What is the HCF of 334,777?
The HCF of 334,777 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 334/78, 777/414?
Answer: GCF of Numerators as per given numbers 334/78, 777/414 is
GCF of Numerators i.e. for 334,777 is 1
LCM of denominators i.e. for 78,414 is 5382.
Thus, GCF of Fractions is 1/5382.Finally, GCF of Fractions for 334/78, 777/414 is 1/5382.