GCF of 643/131, 378/389, 314/431
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 643/131, 378/389, 314/431 i.e 1/21963329 easily. The following is the detailed procedure to determine the greatest common factor of fractions 643/131, 378/389, 314/431.
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 643/131,378/389,314/431?
Given fractions are 643/131,378/389,314/431
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 643/131,378/389,314/431, numerators are 643,378,314
Denominators are 131,389,431
The GCF of 643,378,314 is 1 .
LCM of 131,389,431 is 21963329.
The greatest common factor of 643/131,378/389,314/431 = [GCF of 643,378,314]/[LCM of 131,389,431]= 1/21963329
Therefore, the GCF of 643/131,378/389,314/431 is 1/21963329.
To find the highest common factor of 643,378,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 643 are 1, 643
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The factors of 314 are 1, 2, 157, 314
The HCF of 643,378,314 is 1.
Lets's calculate GCF of 643,378,314
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 643,378,314 By Matching Biggest Common Factor Method
Now, list down the factors of 643
:1,643
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 643,378,314 . The biggest common factor number is the GCF number.
So the greatest common factor 643,378,314 is 1.
Lets's calculate LCM of 131,389,431
Given numbers has no common factors except 1. So, there LCM is their product i.e 21963329
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21963329
Therefore, the GCF of Fractions 643/131,378/389,314/431 is 1/21963329
Least Common Multiple of 131,389,431 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 131,389,431 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(131,389,431) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(131,389,431) x common factors =1 x 1 = 1
LCM(131,389,431) = ( 131 × 389 × 431 ) / 1
LCM(131,389,431) = 21963329 / 1
LCM(131,389,431) = 21963329
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FAQs on GCF of Fractions of 643/131, 378/389, 314/431
1. What is the HCF of 643,378,314?
The HCF of 643,378,314 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 643/131, 378/389, 314/431?
Answer: GCF of Numerators as per given numbers 643/131, 378/389, 314/431 is
GCF of Numerators i.e. for 643,378,314 is 1
LCM of denominators i.e. for 131,389,431 is 21963329.
Thus, GCF of Fractions is 1/21963329.Finally, GCF of Fractions for 643/131, 378/389, 314/431 is 1/21963329.