GCF of 8106/271, 9730/969
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8106/271, 9730/969 i.e 14/262599 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8106/271, 9730/969.
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 8106/271,9730/969?
Given fractions are 8106/271,9730/969
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 8106/271,9730/969, numerators are 8106,9730
Denominators are 271,969
The GCF of 8106,9730 is 14 .
LCM of 271,969 is 262599.
The greatest common factor of 8106/271,9730/969 = [GCF of 8106,9730]/[LCM of 271,969]= 14/262599
Therefore, the GCF of 8106/271,9730/969 is 14/262599.
To find the highest common factor of 8106,9730, we have to find the factors of both numbers and list the highest common factor.
The factors of 8106 are 1, 2, 3, 6, 7, 14, 21, 42, 193, 386, 579, 1158, 1351, 2702, 4053, 8106
The factors of 9730 are 1, 2, 5, 7, 10, 14, 35, 70, 139, 278, 695, 973, 1390, 1946, 4865, 9730
The HCF of 8106,9730 is 14.
Lets's calculate GCF of 8106,9730
| 2 | 8106, 9730 |
| 7 | 4053, 4865 |
| 579, 695 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 8106,9730 By Matching Biggest Common Factor Method
Now, list down the factors of 8106
:1,2,3,6,7,14,21,42,193,386,579,1158,1351,2702,4053,8106
Now, list down the factors of 9730
:1,2,5,7,10,14,35,70,139,278,695,973,1390,1946,4865,9730
Greatest Common Factor
We found the factors 8106,9730 . The biggest common factor number is the GCF number.
So the greatest common factor 8106,9730 is 14.
Lets's calculate LCM of 271,969
Given numbers has no common factors except 1. So, there LCM is their product i.e 262599
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/262599
Therefore, the GCF of Fractions 8106/271,9730/969 is 14/262599
Least Common Multiple of 271,969 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 271,969 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(271,969) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(271,969) x common factors =1 x 1 = 1
LCM(271,969) = ( 271 × 969 ) / 1
LCM(271,969) = 262599 / 1
LCM(271,969) = 262599
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FAQs on GCF of Fractions of 8106/271, 9730/969
1. What is the HCF of 8106,9730?
The HCF of 8106,9730 is 14
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 8106/271, 9730/969?
Answer: GCF of Numerators as per given numbers 8106/271, 9730/969 is
GCF of Numerators i.e. for 8106,9730 is 14
LCM of denominators i.e. for 271,969 is 262599.
Thus, GCF of Fractions is 14/262599.Finally, GCF of Fractions for 8106/271, 9730/969 is 14/262599.