GCF of 198/273, 3234/686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 198/273, 3234/686 i.e 66/26754 easily. The following is the detailed procedure to determine the greatest common factor of fractions 198/273, 3234/686.
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 198/273,3234/686?
Given fractions are 198/273,3234/686
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 198/273,3234/686, numerators are 198,3234
Denominators are 273,686
The GCF of 198,3234 is 66 .
LCM of 273,686 is 26754.
The greatest common factor of 198/273,3234/686 = [GCF of 198,3234]/[LCM of 273,686]= 66/26754
Therefore, the GCF of 198/273,3234/686 is 66/26754.
To find the highest common factor of 198,3234, we have to find the factors of both numbers and list the highest common factor.
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The factors of 3234 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 49, 66, 77, 98, 147, 154, 231, 294, 462, 539, 1078, 1617, 3234
The HCF of 198,3234 is 66.
Lets's calculate GCF of 198,3234
| 2 | 198, 3234 |
| 3 | 99, 1617 |
| 11 | 33, 539 |
| 3, 49 |
∴ So the GCF of the given numbers is 2 x 3 x 11 = 66
Greatest Common Factor of 198,3234 By Matching Biggest Common Factor Method
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Now, list down the factors of 3234
:1,2,3,6,7,11,14,21,22,33,42,49,66,77,98,147,154,231,294,462,539,1078,1617,3234
Greatest Common Factor
We found the factors 198,3234 . The biggest common factor number is the GCF number.
So the greatest common factor 198,3234 is 66.
Lets's calculate LCM of 273,686
| 7 | 273, 686 |
| 39, 98 |
∴ So the LCM of the given numbers is 7 x 39 x 98 = 26754
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 66/26754
Therefore, the GCF of Fractions 198/273,3234/686 is 66/26754
Least Common Multiple of 273,686 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 273,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(273,686) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(273,686) x common factors =7 x 1 = 7
LCM(273,686) = ( 273 × 686 ) / 7
LCM(273,686) = 187278 / 7
LCM(273,686) = 26754
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FAQs on GCF of Fractions of 198/273, 3234/686
1. What is the HCF of 198,3234?
The HCF of 198,3234 is 66
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 198/273, 3234/686?
Answer: GCF of Numerators as per given numbers 198/273, 3234/686 is
GCF of Numerators i.e. for 198,3234 is 66
LCM of denominators i.e. for 273,686 is 26754.
Thus, GCF of Fractions is 66/26754.Finally, GCF of Fractions for 198/273, 3234/686 is 66/26754.