GCF of 298/812, 198/721, 268/309
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 298/812, 198/721, 268/309 i.e 2/250908 easily. The following is the detailed procedure to determine the greatest common factor of fractions 298/812, 198/721, 268/309.
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 298/812,198/721,268/309?
Given fractions are 298/812,198/721,268/309
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 298/812,198/721,268/309, numerators are 298,198,268
Denominators are 812,721,309
The GCF of 298,198,268 is 2 .
LCM of 812,721,309 is 250908.
The greatest common factor of 298/812,198/721,268/309 = [GCF of 298,198,268]/[LCM of 812,721,309]= 2/250908
Therefore, the GCF of 298/812,198/721,268/309 is 2/250908.
To find the highest common factor of 298,198,268, we have to find the factors of both numbers and list the highest common factor.
The factors of 298 are 1, 2, 149, 298
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The factors of 268 are 1, 2, 4, 67, 134, 268
The HCF of 298,198,268 is 2.
Lets's calculate GCF of 298,198,268
| 2 | 298, 198, 268 |
| 149, 99, 134 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 298,198,268 By Matching Biggest Common Factor Method
Now, list down the factors of 298
:1,2,149,298
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 268
:1,2,4,67,134,268
Greatest Common Factor
We found the factors 298,198,268 . The biggest common factor number is the GCF number.
So the greatest common factor 298,198,268 is 2.
Lets's calculate LCM of 812,721,309
| 7 | 812, 721, 309 |
| 103 | 116, 103, 309 |
| 116, 1, 3 |
∴ So the LCM of the given numbers is 7 x 103 x 116 x 1 x 3 = 250908
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/250908
Therefore, the GCF of Fractions 298/812,198/721,268/309 is 2/250908
Least Common Multiple of 812,721,309 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 812,721,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(812,721,309) = 1
common factors(in case of two or more numbers have common factors) = 721
GCF(812,721,309) x common factors =1 x 721 = 721
LCM(812,721,309) = ( 812 × 721 × 309 ) / 721
LCM(812,721,309) = 180904668 / 721
LCM(812,721,309) = 250908
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FAQs on GCF of Fractions of 298/812, 198/721, 268/309
1. What is the HCF of 298,198,268?
The HCF of 298,198,268 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 298/812, 198/721, 268/309?
Answer: GCF of Numerators as per given numbers 298/812, 198/721, 268/309 is
GCF of Numerators i.e. for 298,198,268 is 2
LCM of denominators i.e. for 812,721,309 is 250908.
Thus, GCF of Fractions is 2/250908.Finally, GCF of Fractions for 298/812, 198/721, 268/309 is 2/250908.