Use our free GCF of Fractions Calculator tool to compute the GCF of 35/84, 197/39, 378/419 i.e 1/457548 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/84, 197/39, 378/419.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 35/84,197/39,378/419
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 35/84,197/39,378/419, numerators are 35,197,378
Denominators are 84,39,419
The GCF of 35,197,378 is 1 .
LCM of 84,39,419 is 457548.
The greatest common factor of 35/84,197/39,378/419 = [GCF of 35,197,378]/[LCM of 84,39,419]= 1/457548
Therefore, the GCF of 35/84,197/39,378/419 is 1/457548.
To find the highest common factor of 35,197,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 35 are 1, 5, 7, 35
The factors of 197 are 1, 197
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 35,197,378 is 1.
Lets's calculate GCF of 35,197,378
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 197
:1,197
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 35,197,378 . The biggest common factor number is the GCF number.
So the greatest common factor 35,197,378 is 1.
Lets's calculate LCM of 84,39,419
3 | 84, 39, 419 |
28, 13, 419 |
∴ So the LCM of the given numbers is 3 x 28 x 13 x 419 = 457548
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/457548
Therefore, the GCF of Fractions 35/84,197/39,378/419 is 1/457548
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 84,39,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,39,419) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(84,39,419) x common factors =1 x 3 = 3
LCM(84,39,419) = ( 84 × 39 × 419 ) / 3
LCM(84,39,419) = 1372644 / 3
LCM(84,39,419) = 457548
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 35,197,378?
The HCF of 35,197,378 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 35/84, 197/39, 378/419?
Answer: GCF of Numerators as per given numbers 35/84, 197/39, 378/419 is
GCF of Numerators i.e. for 35,197,378 is 1
LCM of denominators i.e. for 84,39,419 is 457548.
Thus, GCF of Fractions is 1/457548.Finally, GCF of Fractions for 35/84, 197/39, 378/419 is 1/457548.