GCF of 8514/192, 4214/307
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8514/192, 4214/307 i.e 86/58944 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8514/192, 4214/307.
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 8514/192,4214/307?
Given fractions are 8514/192,4214/307
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 8514/192,4214/307, numerators are 8514,4214
Denominators are 192,307
The GCF of 8514,4214 is 86 .
LCM of 192,307 is 58944.
The greatest common factor of 8514/192,4214/307 = [GCF of 8514,4214]/[LCM of 192,307]= 86/58944
Therefore, the GCF of 8514/192,4214/307 is 86/58944.
To find the highest common factor of 8514,4214, we have to find the factors of both numbers and list the highest common factor.
The factors of 8514 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 43, 66, 86, 99, 129, 198, 258, 387, 473, 774, 946, 1419, 2838, 4257, 8514
The factors of 4214 are 1, 2, 7, 14, 43, 49, 86, 98, 301, 602, 2107, 4214
The HCF of 8514,4214 is 86.
Lets's calculate GCF of 8514,4214
| 2 | 8514, 4214 |
| 43 | 4257, 2107 |
| 99, 49 |
∴ So the GCF of the given numbers is 2 x 43 = 86
Greatest Common Factor of 8514,4214 By Matching Biggest Common Factor Method
Now, list down the factors of 8514
:1,2,3,6,9,11,18,22,33,43,66,86,99,129,198,258,387,473,774,946,1419,2838,4257,8514
Now, list down the factors of 4214
:1,2,7,14,43,49,86,98,301,602,2107,4214
Greatest Common Factor
We found the factors 8514,4214 . The biggest common factor number is the GCF number.
So the greatest common factor 8514,4214 is 86.
Lets's calculate LCM of 192,307
Given numbers has no common factors except 1. So, there LCM is their product i.e 58944
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 86/58944
Therefore, the GCF of Fractions 8514/192,4214/307 is 86/58944
Least Common Multiple of 192,307 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 192,307 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(192,307) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(192,307) x common factors =1 x 1 = 1
LCM(192,307) = ( 192 × 307 ) / 1
LCM(192,307) = 58944 / 1
LCM(192,307) = 58944
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FAQs on GCF of Fractions of 8514/192, 4214/307
1. What is the HCF of 8514,4214?
The HCF of 8514,4214 is 86
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 8514/192, 4214/307?
Answer: GCF of Numerators as per given numbers 8514/192, 4214/307 is
GCF of Numerators i.e. for 8514,4214 is 86
LCM of denominators i.e. for 192,307 is 58944.
Thus, GCF of Fractions is 86/58944.Finally, GCF of Fractions for 8514/192, 4214/307 is 86/58944.