Use our free GCF of Fractions Calculator tool to compute the GCF of 238/430, 214/449 i.e 2/193070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 238/430, 214/449.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 238/430,214/449
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 238/430,214/449, numerators are 238,214
Denominators are 430,449
The GCF of 238,214 is 2 .
LCM of 430,449 is 193070.
The greatest common factor of 238/430,214/449 = [GCF of 238,214]/[LCM of 430,449]= 2/193070
Therefore, the GCF of 238/430,214/449 is 2/193070.
To find the highest common factor of 238,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238
The factors of 214 are 1, 2, 107, 214
The HCF of 238,214 is 2.
Lets's calculate GCF of 238,214
2 | 238, 214 |
119, 107 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 238
:1,2,7,14,17,34,119,238
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 238,214 . The biggest common factor number is the GCF number.
So the greatest common factor 238,214 is 2.
Lets's calculate LCM of 430,449
Given numbers has no common factors except 1. So, there LCM is their product i.e 193070
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/193070
Therefore, the GCF of Fractions 238/430,214/449 is 2/193070
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 430,449 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(430,449) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(430,449) x common factors =1 x 1 = 1
LCM(430,449) = ( 430 × 449 ) / 1
LCM(430,449) = 193070 / 1
LCM(430,449) = 193070
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 238,214?
The HCF of 238,214 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 238/430, 214/449?
Answer: GCF of Numerators as per given numbers 238/430, 214/449 is
GCF of Numerators i.e. for 238,214 is 2
LCM of denominators i.e. for 430,449 is 193070.
Thus, GCF of Fractions is 2/193070.Finally, GCF of Fractions for 238/430, 214/449 is 2/193070.