GCF of 134/205, 470/198
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 134/205, 470/198 i.e 2/40590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 134/205, 470/198.
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 134/205,470/198?
Given fractions are 134/205,470/198
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 134/205,470/198, numerators are 134,470
Denominators are 205,198
The GCF of 134,470 is 2 .
LCM of 205,198 is 40590.
The greatest common factor of 134/205,470/198 = [GCF of 134,470]/[LCM of 205,198]= 2/40590
Therefore, the GCF of 134/205,470/198 is 2/40590.
To find the highest common factor of 134,470, we have to find the factors of both numbers and list the highest common factor.
The factors of 134 are 1, 2, 67, 134
The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470
The HCF of 134,470 is 2.
Lets's calculate GCF of 134,470
| 2 | 134, 470 |
| 67, 235 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 134,470 By Matching Biggest Common Factor Method
Now, list down the factors of 134
:1,2,67,134
Now, list down the factors of 470
:1,2,5,10,47,94,235,470
Greatest Common Factor
We found the factors 134,470 . The biggest common factor number is the GCF number.
So the greatest common factor 134,470 is 2.
Lets's calculate LCM of 205,198
Given numbers has no common factors except 1. So, there LCM is their product i.e 40590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/40590
Therefore, the GCF of Fractions 134/205,470/198 is 2/40590
Least Common Multiple of 205,198 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 205,198 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,198) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,198) x common factors =1 x 1 = 1
LCM(205,198) = ( 205 × 198 ) / 1
LCM(205,198) = 40590 / 1
LCM(205,198) = 40590
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FAQs on GCF of Fractions of 134/205, 470/198
1. What is the HCF of 134,470?
The HCF of 134,470 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 134/205, 470/198?
Answer: GCF of Numerators as per given numbers 134/205, 470/198 is
GCF of Numerators i.e. for 134,470 is 2
LCM of denominators i.e. for 205,198 is 40590.
Thus, GCF of Fractions is 2/40590.Finally, GCF of Fractions for 134/205, 470/198 is 2/40590.