GCF of 381/597, 642/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 381/597, 642/414 i.e 3/82386 easily. The following is the detailed procedure to determine the greatest common factor of fractions 381/597, 642/414.
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 381/597,642/414?
Given fractions are 381/597,642/414
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 381/597,642/414, numerators are 381,642
Denominators are 597,414
The GCF of 381,642 is 3 .
LCM of 597,414 is 82386.
The greatest common factor of 381/597,642/414 = [GCF of 381,642]/[LCM of 597,414]= 3/82386
Therefore, the GCF of 381/597,642/414 is 3/82386.
To find the highest common factor of 381,642, we have to find the factors of both numbers and list the highest common factor.
The factors of 381 are 1, 3, 127, 381
The factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642
The HCF of 381,642 is 3.
Lets's calculate GCF of 381,642
| 3 | 381, 642 |
| 127, 214 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 381,642 By Matching Biggest Common Factor Method
Now, list down the factors of 381
:1,3,127,381
Now, list down the factors of 642
:1,2,3,6,107,214,321,642
Greatest Common Factor
We found the factors 381,642 . The biggest common factor number is the GCF number.
So the greatest common factor 381,642 is 3.
Lets's calculate LCM of 597,414
| 3 | 597, 414 |
| 199, 138 |
∴ So the LCM of the given numbers is 3 x 199 x 138 = 82386
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/82386
Therefore, the GCF of Fractions 381/597,642/414 is 3/82386
Least Common Multiple of 597,414 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 597,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(597,414) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(597,414) x common factors =3 x 1 = 3
LCM(597,414) = ( 597 × 414 ) / 3
LCM(597,414) = 247158 / 3
LCM(597,414) = 82386
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FAQs on GCF of Fractions of 381/597, 642/414
1. What is the HCF of 381,642?
The HCF of 381,642 is 3
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 381/597, 642/414?
Answer: GCF of Numerators as per given numbers 381/597, 642/414 is
GCF of Numerators i.e. for 381,642 is 3
LCM of denominators i.e. for 597,414 is 82386.
Thus, GCF of Fractions is 3/82386.Finally, GCF of Fractions for 381/597, 642/414 is 3/82386.