GCF of 810/766, 2214/497
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 810/766, 2214/497 i.e 54/380702 easily. The following is the detailed procedure to determine the greatest common factor of fractions 810/766, 2214/497.
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 810/766,2214/497?
Given fractions are 810/766,2214/497
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 810/766,2214/497, numerators are 810,2214
Denominators are 766,497
The GCF of 810,2214 is 54 .
LCM of 766,497 is 380702.
The greatest common factor of 810/766,2214/497 = [GCF of 810,2214]/[LCM of 766,497]= 54/380702
Therefore, the GCF of 810/766,2214/497 is 54/380702.
To find the highest common factor of 810,2214, we have to find the factors of both numbers and list the highest common factor.
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The factors of 2214 are 1, 2, 3, 6, 9, 18, 27, 41, 54, 82, 123, 246, 369, 738, 1107, 2214
The HCF of 810,2214 is 54.
Lets's calculate GCF of 810,2214
| 2 | 810, 2214 |
| 3 | 405, 1107 |
| 3 | 135, 369 |
| 3 | 45, 123 |
| 15, 41 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 3 = 54
Greatest Common Factor of 810,2214 By Matching Biggest Common Factor Method
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Now, list down the factors of 2214
:1,2,3,6,9,18,27,41,54,82,123,246,369,738,1107,2214
Greatest Common Factor
We found the factors 810,2214 . The biggest common factor number is the GCF number.
So the greatest common factor 810,2214 is 54.
Lets's calculate LCM of 766,497
Given numbers has no common factors except 1. So, there LCM is their product i.e 380702
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 54/380702
Therefore, the GCF of Fractions 810/766,2214/497 is 54/380702
Least Common Multiple of 766,497 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 766,497 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(766,497) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(766,497) x common factors =1 x 1 = 1
LCM(766,497) = ( 766 × 497 ) / 1
LCM(766,497) = 380702 / 1
LCM(766,497) = 380702
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FAQs on GCF of Fractions of 810/766, 2214/497
1. What is the HCF of 810,2214?
The HCF of 810,2214 is 54
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 810/766, 2214/497?
Answer: GCF of Numerators as per given numbers 810/766, 2214/497 is
GCF of Numerators i.e. for 810,2214 is 54
LCM of denominators i.e. for 766,497 is 380702.
Thus, GCF of Fractions is 54/380702.Finally, GCF of Fractions for 810/766, 2214/497 is 54/380702.