GCF of 494/197, 209/305
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 494/197, 209/305 i.e 19/60085 easily. The following is the detailed procedure to determine the greatest common factor of fractions 494/197, 209/305.
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 494/197,209/305?
Given fractions are 494/197,209/305
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 494/197,209/305, numerators are 494,209
Denominators are 197,305
The GCF of 494,209 is 19 .
LCM of 197,305 is 60085.
The greatest common factor of 494/197,209/305 = [GCF of 494,209]/[LCM of 197,305]= 19/60085
Therefore, the GCF of 494/197,209/305 is 19/60085.
To find the highest common factor of 494,209, we have to find the factors of both numbers and list the highest common factor.
The factors of 494 are 1, 2, 13, 19, 26, 38, 247, 494
The factors of 209 are 1, 11, 19, 209
The HCF of 494,209 is 19.
Lets's calculate GCF of 494,209
| 19 | 494, 209 |
| 26, 11 |
∴ So the GCF of the given numbers is 19 = 19
Greatest Common Factor of 494,209 By Matching Biggest Common Factor Method
Now, list down the factors of 494
:1,2,13,19,26,38,247,494
Now, list down the factors of 209
:1,11,19,209
Greatest Common Factor
We found the factors 494,209 . The biggest common factor number is the GCF number.
So the greatest common factor 494,209 is 19.
Lets's calculate LCM of 197,305
Given numbers has no common factors except 1. So, there LCM is their product i.e 60085
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/60085
Therefore, the GCF of Fractions 494/197,209/305 is 19/60085
Least Common Multiple of 197,305 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 197,305 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(197,305) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(197,305) x common factors =1 x 1 = 1
LCM(197,305) = ( 197 × 305 ) / 1
LCM(197,305) = 60085 / 1
LCM(197,305) = 60085
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FAQs on GCF of Fractions of 494/197, 209/305
1. What is the HCF of 494,209?
The HCF of 494,209 is 19
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 494/197, 209/305?
Answer: GCF of Numerators as per given numbers 494/197, 209/305 is
GCF of Numerators i.e. for 494,209 is 19
LCM of denominators i.e. for 197,305 is 60085.
Thus, GCF of Fractions is 19/60085.Finally, GCF of Fractions for 494/197, 209/305 is 19/60085.