GCF of 8246/287, 9730/770
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8246/287, 9730/770 i.e 14/31570 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8246/287, 9730/770.
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 8246/287,9730/770?
Given fractions are 8246/287,9730/770
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 8246/287,9730/770, numerators are 8246,9730
Denominators are 287,770
The GCF of 8246,9730 is 14 .
LCM of 287,770 is 31570.
The greatest common factor of 8246/287,9730/770 = [GCF of 8246,9730]/[LCM of 287,770]= 14/31570
Therefore, the GCF of 8246/287,9730/770 is 14/31570.
To find the highest common factor of 8246,9730, we have to find the factors of both numbers and list the highest common factor.
The factors of 8246 are 1, 2, 7, 14, 19, 31, 38, 62, 133, 217, 266, 434, 589, 1178, 4123, 8246
The factors of 9730 are 1, 2, 5, 7, 10, 14, 35, 70, 139, 278, 695, 973, 1390, 1946, 4865, 9730
The HCF of 8246,9730 is 14.
Lets's calculate GCF of 8246,9730
| 2 | 8246, 9730 |
| 7 | 4123, 4865 |
| 589, 695 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 8246,9730 By Matching Biggest Common Factor Method
Now, list down the factors of 8246
:1,2,7,14,19,31,38,62,133,217,266,434,589,1178,4123,8246
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 8246,9730 . The biggest common factor number is the GCF number.
So the greatest common factor 8246,9730 is 14.
Lets's calculate LCM of 287,770
| 7 | 287, 770 |
| 41, 110 |
∴ So the LCM of the given numbers is 7 x 41 x 110 = 31570
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/31570
Therefore, the GCF of Fractions 8246/287,9730/770 is 14/31570
Least Common Multiple of 287,770 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 287,770 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(287,770) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(287,770) x common factors =7 x 1 = 7
LCM(287,770) = ( 287 × 770 ) / 7
LCM(287,770) = 220990 / 7
LCM(287,770) = 31570
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FAQs on GCF of Fractions of 8246/287, 9730/770
1. What is the HCF of 8246,9730?
The HCF of 8246,9730 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 8246/287, 9730/770?
Answer: GCF of Numerators as per given numbers 8246/287, 9730/770 is
GCF of Numerators i.e. for 8246,9730 is 14
LCM of denominators i.e. for 287,770 is 31570.
Thus, GCF of Fractions is 14/31570.Finally, GCF of Fractions for 8246/287, 9730/770 is 14/31570.