Use our free GCF of Fractions Calculator tool to compute the GCF of 128/113, 214/159 i.e 2/17967 easily. The following is the detailed procedure to determine the greatest common factor of fractions 128/113, 214/159.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 128/113,214/159
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 128/113,214/159, numerators are 128,214
Denominators are 113,159
The GCF of 128,214 is 2 .
LCM of 113,159 is 17967.
The greatest common factor of 128/113,214/159 = [GCF of 128,214]/[LCM of 113,159]= 2/17967
Therefore, the GCF of 128/113,214/159 is 2/17967.
To find the highest common factor of 128,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
The factors of 214 are 1, 2, 107, 214
The HCF of 128,214 is 2.
Lets's calculate GCF of 128,214
2 | 128, 214 |
64, 107 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 128
:1,2,4,8,16,32,64,128
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 128,214 . The biggest common factor number is the GCF number.
So the greatest common factor 128,214 is 2.
Lets's calculate LCM of 113,159
Given numbers has no common factors except 1. So, there LCM is their product i.e 17967
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/17967
Therefore, the GCF of Fractions 128/113,214/159 is 2/17967
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 113,159 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(113,159) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(113,159) x common factors =1 x 1 = 1
LCM(113,159) = ( 113 × 159 ) / 1
LCM(113,159) = 17967 / 1
LCM(113,159) = 17967
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 128,214?
The HCF of 128,214 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 128/113, 214/159?
Answer: GCF of Numerators as per given numbers 128/113, 214/159 is
GCF of Numerators i.e. for 128,214 is 2
LCM of denominators i.e. for 113,159 is 17967.
Thus, GCF of Fractions is 2/17967.Finally, GCF of Fractions for 128/113, 214/159 is 2/17967.