GCF of 306/414, 7857/8210
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 306/414, 7857/8210 i.e 9/1699470 easily. The following is the detailed procedure to determine the greatest common factor of fractions 306/414, 7857/8210.
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 306/414,7857/8210?
Given fractions are 306/414,7857/8210
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 306/414,7857/8210, numerators are 306,7857
Denominators are 414,8210
The GCF of 306,7857 is 9 .
LCM of 414,8210 is 1699470.
The greatest common factor of 306/414,7857/8210 = [GCF of 306,7857]/[LCM of 414,8210]= 9/1699470
Therefore, the GCF of 306/414,7857/8210 is 9/1699470.
To find the highest common factor of 306,7857, we have to find the factors of both numbers and list the highest common factor.
The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
The factors of 7857 are 1, 3, 9, 27, 81, 97, 291, 873, 2619, 7857
The HCF of 306,7857 is 9.
Lets's calculate GCF of 306,7857
| 3 | 306, 7857 |
| 3 | 102, 2619 |
| 34, 873 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 306,7857 By Matching Biggest Common Factor Method
Now, list down the factors of 306
:1,2,3,6,9,17,18,34,51,102,153,306
Now, list down the factors of 7857
:1,3,9,27,81,97,291,873,2619,7857
Greatest Common Factor
We found the factors 306,7857 . The biggest common factor number is the GCF number.
So the greatest common factor 306,7857 is 9.
Lets's calculate LCM of 414,8210
| 2 | 414, 8210 |
| 207, 4105 |
∴ So the LCM of the given numbers is 2 x 207 x 4105 = 1699470
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/1699470
Therefore, the GCF of Fractions 306/414,7857/8210 is 9/1699470
Least Common Multiple of 414,8210 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 414,8210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,8210) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,8210) x common factors =2 x 1 = 2
LCM(414,8210) = ( 414 × 8210 ) / 2
LCM(414,8210) = 3398940 / 2
LCM(414,8210) = 1699470
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FAQs on GCF of Fractions of 306/414, 7857/8210
1. What is the HCF of 306,7857?
The HCF of 306,7857 is 9
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 306/414, 7857/8210?
Answer: GCF of Numerators as per given numbers 306/414, 7857/8210 is
GCF of Numerators i.e. for 306,7857 is 9
LCM of denominators i.e. for 414,8210 is 1699470.
Thus, GCF of Fractions is 9/1699470.Finally, GCF of Fractions for 306/414, 7857/8210 is 9/1699470.