GCF of 342/738, 7714/729
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 342/738, 7714/729 i.e 38/59778 easily. The following is the detailed procedure to determine the greatest common factor of fractions 342/738, 7714/729.
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 342/738,7714/729?
Given fractions are 342/738,7714/729
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 342/738,7714/729, numerators are 342,7714
Denominators are 738,729
The GCF of 342,7714 is 38 .
LCM of 738,729 is 59778.
The greatest common factor of 342/738,7714/729 = [GCF of 342,7714]/[LCM of 738,729]= 38/59778
Therefore, the GCF of 342/738,7714/729 is 38/59778.
To find the highest common factor of 342,7714, we have to find the factors of both numbers and list the highest common factor.
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The factors of 7714 are 1, 2, 7, 14, 19, 29, 38, 58, 133, 203, 266, 406, 551, 1102, 3857, 7714
The HCF of 342,7714 is 38.
Lets's calculate GCF of 342,7714
| 2 | 342, 7714 |
| 19 | 171, 3857 |
| 9, 203 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 342,7714 By Matching Biggest Common Factor Method
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Now, list down the factors of 7714
:1,2,7,14,19,29,38,58,133,203,266,406,551,1102,3857,7714
Greatest Common Factor
We found the factors 342,7714 . The biggest common factor number is the GCF number.
So the greatest common factor 342,7714 is 38.
Lets's calculate LCM of 738,729
| 3 | 738, 729 |
| 3 | 246, 243 |
| 82, 81 |
∴ So the LCM of the given numbers is 3 x 3 x 82 x 81 = 59778
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/59778
Therefore, the GCF of Fractions 342/738,7714/729 is 38/59778
Least Common Multiple of 738,729 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 738,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(738,729) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(738,729) x common factors =9 x 1 = 9
LCM(738,729) = ( 738 × 729 ) / 9
LCM(738,729) = 538002 / 9
LCM(738,729) = 59778
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FAQs on GCF of Fractions of 342/738, 7714/729
1. What is the HCF of 342,7714?
The HCF of 342,7714 is 38
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 342/738, 7714/729?
Answer: GCF of Numerators as per given numbers 342/738, 7714/729 is
GCF of Numerators i.e. for 342,7714 is 38
LCM of denominators i.e. for 738,729 is 59778.
Thus, GCF of Fractions is 38/59778.Finally, GCF of Fractions for 342/738, 7714/729 is 38/59778.