Use our free GCF of Fractions Calculator tool to compute the GCF of 212/341, 654/413 i.e 2/140833 easily. The following is the detailed procedure to determine the greatest common factor of fractions 212/341, 654/413.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 212/341,654/413
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 212/341,654/413, numerators are 212,654
Denominators are 341,413
The GCF of 212,654 is 2 .
LCM of 341,413 is 140833.
The greatest common factor of 212/341,654/413 = [GCF of 212,654]/[LCM of 341,413]= 2/140833
Therefore, the GCF of 212/341,654/413 is 2/140833.
To find the highest common factor of 212,654, we have to find the factors of both numbers and list the highest common factor.
The factors of 212 are 1, 2, 4, 53, 106, 212
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The HCF of 212,654 is 2.
Lets's calculate GCF of 212,654
2 | 212, 654 |
106, 327 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 212
:1,2,4,53,106,212
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Greatest Common Factor
We found the factors 212,654 . The biggest common factor number is the GCF number.
So the greatest common factor 212,654 is 2.
Lets's calculate LCM of 341,413
Given numbers has no common factors except 1. So, there LCM is their product i.e 140833
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/140833
Therefore, the GCF of Fractions 212/341,654/413 is 2/140833
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 341,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(341,413) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(341,413) x common factors =1 x 1 = 1
LCM(341,413) = ( 341 × 413 ) / 1
LCM(341,413) = 140833 / 1
LCM(341,413) = 140833
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 212,654?
The HCF of 212,654 is 2
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 212/341, 654/413?
Answer: GCF of Numerators as per given numbers 212/341, 654/413 is
GCF of Numerators i.e. for 212,654 is 2
LCM of denominators i.e. for 341,413 is 140833.
Thus, GCF of Fractions is 2/140833.Finally, GCF of Fractions for 212/341, 654/413 is 2/140833.