GCF of 8138/690, 7286/9678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8138/690, 7286/9678 i.e 2/1112970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8138/690, 7286/9678.
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 8138/690,7286/9678?
Given fractions are 8138/690,7286/9678
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 8138/690,7286/9678, numerators are 8138,7286
Denominators are 690,9678
The GCF of 8138,7286 is 2 .
LCM of 690,9678 is 1112970.
The greatest common factor of 8138/690,7286/9678 = [GCF of 8138,7286]/[LCM of 690,9678]= 2/1112970
Therefore, the GCF of 8138/690,7286/9678 is 2/1112970.
To find the highest common factor of 8138,7286, we have to find the factors of both numbers and list the highest common factor.
The factors of 8138 are 1, 2, 13, 26, 313, 626, 4069, 8138
The factors of 7286 are 1, 2, 3643, 7286
The HCF of 8138,7286 is 2.
Lets's calculate GCF of 8138,7286
| 2 | 8138, 7286 |
| 4069, 3643 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8138,7286 By Matching Biggest Common Factor Method
Now, list down the factors of 8138
:1,2,13,26,313,626,4069,8138
Now, list down the factors of 7286
:1,2,3643,7286
Greatest Common Factor
We found the factors 8138,7286 . The biggest common factor number is the GCF number.
So the greatest common factor 8138,7286 is 2.
Lets's calculate LCM of 690,9678
| 2 | 690, 9678 |
| 3 | 345, 4839 |
| 115, 1613 |
∴ So the LCM of the given numbers is 2 x 3 x 115 x 1613 = 1112970
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1112970
Therefore, the GCF of Fractions 8138/690,7286/9678 is 2/1112970
Least Common Multiple of 690,9678 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 690,9678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(690,9678) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(690,9678) x common factors =6 x 1 = 6
LCM(690,9678) = ( 690 × 9678 ) / 6
LCM(690,9678) = 6677820 / 6
LCM(690,9678) = 1112970
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FAQs on GCF of Fractions of 8138/690, 7286/9678
1. What is the HCF of 8138,7286?
The HCF of 8138,7286 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 8138/690, 7286/9678?
Answer: GCF of Numerators as per given numbers 8138/690, 7286/9678 is
GCF of Numerators i.e. for 8138,7286 is 2
LCM of denominators i.e. for 690,9678 is 1112970.
Thus, GCF of Fractions is 2/1112970.Finally, GCF of Fractions for 8138/690, 7286/9678 is 2/1112970.