GCF of 9712/304, 6848/4314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9712/304, 6848/4314 i.e 16/655728 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9712/304, 6848/4314.
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 9712/304,6848/4314?
Given fractions are 9712/304,6848/4314
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 9712/304,6848/4314, numerators are 9712,6848
Denominators are 304,4314
The GCF of 9712,6848 is 16 .
LCM of 304,4314 is 655728.
The greatest common factor of 9712/304,6848/4314 = [GCF of 9712,6848]/[LCM of 304,4314]= 16/655728
Therefore, the GCF of 9712/304,6848/4314 is 16/655728.
To find the highest common factor of 9712,6848, we have to find the factors of both numbers and list the highest common factor.
The factors of 9712 are 1, 2, 4, 8, 16, 607, 1214, 2428, 4856, 9712
The factors of 6848 are 1, 2, 4, 8, 16, 32, 64, 107, 214, 428, 856, 1712, 3424, 6848
The HCF of 9712,6848 is 16.
Lets's calculate GCF of 9712,6848
| 2 | 9712, 6848 |
| 2 | 4856, 3424 |
| 2 | 2428, 1712 |
| 2 | 1214, 856 |
| 607, 428 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 9712,6848 By Matching Biggest Common Factor Method
Now, list down the factors of 9712
:1,2,4,8,16,607,1214,2428,4856,9712
Now, list down the factors of 6848
:1,2,4,8,16,32,64,107,214,428,856,1712,3424,6848
Greatest Common Factor
We found the factors 9712,6848 . The biggest common factor number is the GCF number.
So the greatest common factor 9712,6848 is 16.
Lets's calculate LCM of 304,4314
| 2 | 304, 4314 |
| 152, 2157 |
∴ So the LCM of the given numbers is 2 x 152 x 2157 = 655728
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/655728
Therefore, the GCF of Fractions 9712/304,6848/4314 is 16/655728
Least Common Multiple of 304,4314 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 304,4314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(304,4314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(304,4314) x common factors =2 x 1 = 2
LCM(304,4314) = ( 304 × 4314 ) / 2
LCM(304,4314) = 1311456 / 2
LCM(304,4314) = 655728
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FAQs on GCF of Fractions of 9712/304, 6848/4314
1. What is the HCF of 9712,6848?
The HCF of 9712,6848 is 16
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 9712/304, 6848/4314?
Answer: GCF of Numerators as per given numbers 9712/304, 6848/4314 is
GCF of Numerators i.e. for 9712,6848 is 16
LCM of denominators i.e. for 304,4314 is 655728.
Thus, GCF of Fractions is 16/655728.Finally, GCF of Fractions for 9712/304, 6848/4314 is 16/655728.