GCF of 419/186, 821/218
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 419/186, 821/218 i.e 1/20274 easily. The following is the detailed procedure to determine the greatest common factor of fractions 419/186, 821/218.
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 419/186,821/218?
Given fractions are 419/186,821/218
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 419/186,821/218, numerators are 419,821
Denominators are 186,218
The GCF of 419,821 is 1 .
LCM of 186,218 is 20274.
The greatest common factor of 419/186,821/218 = [GCF of 419,821]/[LCM of 186,218]= 1/20274
Therefore, the GCF of 419/186,821/218 is 1/20274.
To find the highest common factor of 419,821, we have to find the factors of both numbers and list the highest common factor.
The factors of 419 are 1, 419
The factors of 821 are 1, 821
The HCF of 419,821 is 1.
Lets's calculate GCF of 419,821
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 419,821 By Matching Biggest Common Factor Method
Now, list down the factors of 419
:1,419
Now, list down the factors of 821
:1,821
Greatest Common Factor
We found the factors 419,821 . The biggest common factor number is the GCF number.
So the greatest common factor 419,821 is 1.
Lets's calculate LCM of 186,218
| 2 | 186, 218 |
| 93, 109 |
∴ So the LCM of the given numbers is 2 x 93 x 109 = 20274
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/20274
Therefore, the GCF of Fractions 419/186,821/218 is 1/20274
Least Common Multiple of 186,218 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 186,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(186,218) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(186,218) x common factors =2 x 1 = 2
LCM(186,218) = ( 186 × 218 ) / 2
LCM(186,218) = 40548 / 2
LCM(186,218) = 20274
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FAQs on GCF of Fractions of 419/186, 821/218
1. What is the HCF of 419,821?
The HCF of 419,821 is 1
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 419/186, 821/218?
Answer: GCF of Numerators as per given numbers 419/186, 821/218 is
GCF of Numerators i.e. for 419,821 is 1
LCM of denominators i.e. for 186,218 is 20274.
Thus, GCF of Fractions is 1/20274.Finally, GCF of Fractions for 419/186, 821/218 is 1/20274.