Use our free GCF of Fractions Calculator tool to compute the GCF of 406/242, 8360/619 i.e 2/149798 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/242, 8360/619.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 406/242,8360/619
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 406/242,8360/619, numerators are 406,8360
Denominators are 242,619
The GCF of 406,8360 is 2 .
LCM of 242,619 is 149798.
The greatest common factor of 406/242,8360/619 = [GCF of 406,8360]/[LCM of 242,619]= 2/149798
Therefore, the GCF of 406/242,8360/619 is 2/149798.
To find the highest common factor of 406,8360, we have to find the factors of both numbers and list the highest common factor.
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The factors of 8360 are 1, 2, 4, 5, 8, 10, 11, 19, 20, 22, 38, 40, 44, 55, 76, 88, 95, 110, 152, 190, 209, 220, 380, 418, 440, 760, 836, 1045, 1672, 2090, 4180, 8360
The HCF of 406,8360 is 2.
Lets's calculate GCF of 406,8360
2 | 406, 8360 |
203, 4180 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Now, list down the factors of 8360
:1,2,4,5,8,10,11,19,20,22,38,40,44,55,76,88,95,110,152,190,209,220,380,418,440,760,836,1045,1672,2090,4180,8360
Greatest Common Factor
We found the factors 406,8360 . The biggest common factor number is the GCF number.
So the greatest common factor 406,8360 is 2.
Lets's calculate LCM of 242,619
Given numbers has no common factors except 1. So, there LCM is their product i.e 149798
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/149798
Therefore, the GCF of Fractions 406/242,8360/619 is 2/149798
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 242,619 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(242,619) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(242,619) x common factors =1 x 1 = 1
LCM(242,619) = ( 242 × 619 ) / 1
LCM(242,619) = 149798 / 1
LCM(242,619) = 149798
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 406,8360?
The HCF of 406,8360 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 406/242, 8360/619?
Answer: GCF of Numerators as per given numbers 406/242, 8360/619 is
GCF of Numerators i.e. for 406,8360 is 2
LCM of denominators i.e. for 242,619 is 149798.
Thus, GCF of Fractions is 2/149798.Finally, GCF of Fractions for 406/242, 8360/619 is 2/149798.