Use our free GCF of Fractions Calculator tool to compute the GCF of 338/104, 414/135 i.e 2/14040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 338/104, 414/135.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 338/104,414/135
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 338/104,414/135, numerators are 338,414
Denominators are 104,135
The GCF of 338,414 is 2 .
LCM of 104,135 is 14040.
The greatest common factor of 338/104,414/135 = [GCF of 338,414]/[LCM of 104,135]= 2/14040
Therefore, the GCF of 338/104,414/135 is 2/14040.
To find the highest common factor of 338,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 338 are 1, 2, 13, 26, 169, 338
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 338,414 is 2.
Lets's calculate GCF of 338,414
2 | 338, 414 |
169, 207 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 338
:1,2,13,26,169,338
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 338,414 . The biggest common factor number is the GCF number.
So the greatest common factor 338,414 is 2.
Lets's calculate LCM of 104,135
Given numbers has no common factors except 1. So, there LCM is their product i.e 14040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/14040
Therefore, the GCF of Fractions 338/104,414/135 is 2/14040
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 104,135 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(104,135) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(104,135) x common factors =1 x 1 = 1
LCM(104,135) = ( 104 × 135 ) / 1
LCM(104,135) = 14040 / 1
LCM(104,135) = 14040
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 338,414?
The HCF of 338,414 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 338/104, 414/135?
Answer: GCF of Numerators as per given numbers 338/104, 414/135 is
GCF of Numerators i.e. for 338,414 is 2
LCM of denominators i.e. for 104,135 is 14040.
Thus, GCF of Fractions is 2/14040.Finally, GCF of Fractions for 338/104, 414/135 is 2/14040.