Use our free GCF of Fractions Calculator tool to compute the GCF of 50/20, 81/55, 70/98, 21/57 i.e 1/614460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 50/20, 81/55, 70/98, 21/57.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 50/20,81/55,70/98,21/57
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 50/20,81/55,70/98,21/57, numerators are 50,81,70,21
Denominators are 20,55,98,57
The GCF of 50,81,70,21 is 1 .
LCM of 20,55,98,57 is 614460.
The greatest common factor of 50/20,81/55,70/98,21/57 = [GCF of 50,81,70,21]/[LCM of 20,55,98,57]= 1/614460
Therefore, the GCF of 50/20,81/55,70/98,21/57 is 1/614460.
To find the highest common factor of 50,81,70,21, we have to find the factors of both numbers and list the highest common factor.
The factors of 50 are 1, 2, 5, 10, 25, 50
The factors of 81 are 1, 3, 9, 27, 81
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 21 are 1, 3, 7, 21
The HCF of 50,81,70,21 is 1.
Lets's calculate GCF of 50,81,70,21
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 50
:1,2,5,10,25,50
Now, list down the factors of 81
:1,3,9,27,81
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 21
:1,3,7,21
Greatest Common Factor
We found the factors 50,81,70,21 . The biggest common factor number is the GCF number.
So the greatest common factor 50,81,70,21 is 1.
Lets's calculate LCM of 20,55,98,57
2 | 20, 55, 98, 57 |
5 | 10, 55, 49, 57 |
2, 11, 49, 57 |
∴ So the LCM of the given numbers is 2 x 5 x 2 x 11 x 49 x 57 = 614460
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/614460
Therefore, the GCF of Fractions 50/20,81/55,70/98,21/57 is 1/614460
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 20,55,98,57 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,55,98,57) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(20,55,98,57) x common factors =1 x 10 = 10
LCM(20,55,98,57) = ( 20 × 55 × 98 × 57 ) / 10
LCM(20,55,98,57) = 6144600 / 10
LCM(20,55,98,57) = 614460
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 50,81,70,21?
The HCF of 50,81,70,21 is 1
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 50/20, 81/55, 70/98, 21/57?
Answer: GCF of Numerators as per given numbers 50/20, 81/55, 70/98, 21/57 is
GCF of Numerators i.e. for 50,81,70,21 is 1
LCM of denominators i.e. for 20,55,98,57 is 614460.
Thus, GCF of Fractions is 1/614460.Finally, GCF of Fractions for 50/20, 81/55, 70/98, 21/57 is 1/614460.