GCF of 419/35, 354/413
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 419/35, 354/413 i.e 1/2065 easily. The following is the detailed procedure to determine the greatest common factor of fractions 419/35, 354/413.
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 419/35,354/413?
Given fractions are 419/35,354/413
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 419/35,354/413, numerators are 419,354
Denominators are 35,413
The GCF of 419,354 is 1 .
LCM of 35,413 is 2065.
The greatest common factor of 419/35,354/413 = [GCF of 419,354]/[LCM of 35,413]= 1/2065
Therefore, the GCF of 419/35,354/413 is 1/2065.
To find the highest common factor of 419,354, 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 354 are 1, 2, 3, 6, 59, 118, 177, 354
The HCF of 419,354 is 1.
Lets's calculate GCF of 419,354
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 419,354 By Matching Biggest Common Factor Method
Now, list down the factors of 419
:1,419
Now, list down the factors of 354
:1,2,3,6,59,118,177,354
Greatest Common Factor
We found the factors 419,354 . The biggest common factor number is the GCF number.
So the greatest common factor 419,354 is 1.
Lets's calculate LCM of 35,413
| 7 | 35, 413 |
| 5, 59 |
∴ So the LCM of the given numbers is 7 x 5 x 59 = 2065
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2065
Therefore, the GCF of Fractions 419/35,354/413 is 1/2065
Least Common Multiple of 35,413 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 35,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,413) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(35,413) x common factors =7 x 1 = 7
LCM(35,413) = ( 35 × 413 ) / 7
LCM(35,413) = 14455 / 7
LCM(35,413) = 2065
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FAQs on GCF of Fractions of 419/35, 354/413
1. What is the HCF of 419,354?
The HCF of 419,354 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 419/35, 354/413?
Answer: GCF of Numerators as per given numbers 419/35, 354/413 is
GCF of Numerators i.e. for 419,354 is 1
LCM of denominators i.e. for 35,413 is 2065.
Thus, GCF of Fractions is 1/2065.Finally, GCF of Fractions for 419/35, 354/413 is 1/2065.