GCF of 806/414, 6754/724
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 806/414, 6754/724 i.e 2/149868 easily. The following is the detailed procedure to determine the greatest common factor of fractions 806/414, 6754/724.
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 806/414,6754/724?
Given fractions are 806/414,6754/724
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 806/414,6754/724, numerators are 806,6754
Denominators are 414,724
The GCF of 806,6754 is 2 .
LCM of 414,724 is 149868.
The greatest common factor of 806/414,6754/724 = [GCF of 806,6754]/[LCM of 414,724]= 2/149868
Therefore, the GCF of 806/414,6754/724 is 2/149868.
To find the highest common factor of 806,6754, we have to find the factors of both numbers and list the highest common factor.
The factors of 806 are 1, 2, 13, 26, 31, 62, 403, 806
The factors of 6754 are 1, 2, 11, 22, 307, 614, 3377, 6754
The HCF of 806,6754 is 2.
Lets's calculate GCF of 806,6754
| 2 | 806, 6754 |
| 403, 3377 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 806,6754 By Matching Biggest Common Factor Method
Now, list down the factors of 806
:1,2,13,26,31,62,403,806
Now, list down the factors of 6754
:1,2,11,22,307,614,3377,6754
Greatest Common Factor
We found the factors 806,6754 . The biggest common factor number is the GCF number.
So the greatest common factor 806,6754 is 2.
Lets's calculate LCM of 414,724
| 2 | 414, 724 |
| 207, 362 |
∴ So the LCM of the given numbers is 2 x 207 x 362 = 149868
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/149868
Therefore, the GCF of Fractions 806/414,6754/724 is 2/149868
Least Common Multiple of 414,724 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 414,724 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,724) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,724) x common factors =2 x 1 = 2
LCM(414,724) = ( 414 × 724 ) / 2
LCM(414,724) = 299736 / 2
LCM(414,724) = 149868
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FAQs on GCF of Fractions of 806/414, 6754/724
1. What is the HCF of 806,6754?
The HCF of 806,6754 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 806/414, 6754/724?
Answer: GCF of Numerators as per given numbers 806/414, 6754/724 is
GCF of Numerators i.e. for 806,6754 is 2
LCM of denominators i.e. for 414,724 is 149868.
Thus, GCF of Fractions is 2/149868.Finally, GCF of Fractions for 806/414, 6754/724 is 2/149868.