GCF of 364/342, 238/298
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 364/342, 238/298 i.e 14/50958 easily. The following is the detailed procedure to determine the greatest common factor of fractions 364/342, 238/298.
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 364/342,238/298?
Given fractions are 364/342,238/298
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 364/342,238/298, numerators are 364,238
Denominators are 342,298
The GCF of 364,238 is 14 .
LCM of 342,298 is 50958.
The greatest common factor of 364/342,238/298 = [GCF of 364,238]/[LCM of 342,298]= 14/50958
Therefore, the GCF of 364/342,238/298 is 14/50958.
To find the highest common factor of 364,238, we have to find the factors of both numbers and list the highest common factor.
The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238
The HCF of 364,238 is 14.
Lets's calculate GCF of 364,238
| 2 | 364, 238 |
| 7 | 182, 119 |
| 26, 17 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 364,238 By Matching Biggest Common Factor Method
Now, list down the factors of 364
:1,2,4,7,13,14,26,28,52,91,182,364
Now, list down the factors of 238
:1,2,7,14,17,34,119,238
Greatest Common Factor
We found the factors 364,238 . The biggest common factor number is the GCF number.
So the greatest common factor 364,238 is 14.
Lets's calculate LCM of 342,298
| 2 | 342, 298 |
| 171, 149 |
∴ So the LCM of the given numbers is 2 x 171 x 149 = 50958
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/50958
Therefore, the GCF of Fractions 364/342,238/298 is 14/50958
Least Common Multiple of 342,298 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 342,298 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,298) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(342,298) x common factors =2 x 1 = 2
LCM(342,298) = ( 342 × 298 ) / 2
LCM(342,298) = 101916 / 2
LCM(342,298) = 50958
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FAQs on GCF of Fractions of 364/342, 238/298
1. What is the HCF of 364,238?
The HCF of 364,238 is 14
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 364/342, 238/298?
Answer: GCF of Numerators as per given numbers 364/342, 238/298 is
GCF of Numerators i.e. for 364,238 is 14
LCM of denominators i.e. for 342,298 is 50958.
Thus, GCF of Fractions is 14/50958.Finally, GCF of Fractions for 364/342, 238/298 is 14/50958.