Use our free GCF of Fractions Calculator tool to compute the GCF of 64/21, 192/75, 270/245 i.e 2/3675 easily. The following is the detailed procedure to determine the greatest common factor of fractions 64/21, 192/75, 270/245.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 64/21,192/75,270/245
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 64/21,192/75,270/245, numerators are 64,192,270
Denominators are 21,75,245
The GCF of 64,192,270 is 2 .
LCM of 21,75,245 is 3675.
The greatest common factor of 64/21,192/75,270/245 = [GCF of 64,192,270]/[LCM of 21,75,245]= 2/3675
Therefore, the GCF of 64/21,192/75,270/245 is 2/3675.
To find the highest common factor of 64,192,270, we have to find the factors of both numbers and list the highest common factor.
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The HCF of 64,192,270 is 2.
Lets's calculate GCF of 64,192,270
2 | 64, 192, 270 |
32, 96, 135 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 192
:1,2,3,4,6,8,12,16,24,32,48,64,96,192
Now, list down the factors of 270
:1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270
Greatest Common Factor
We found the factors 64,192,270 . The biggest common factor number is the GCF number.
So the greatest common factor 64,192,270 is 2.
Lets's calculate LCM of 21,75,245
3 | 21, 75, 245 |
5 | 7, 25, 245 |
7 | 7, 5, 49 |
1, 5, 7 |
∴ So the LCM of the given numbers is 3 x 5 x 7 x 1 x 5 x 7 = 3675
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3675
Therefore, the GCF of Fractions 64/21,192/75,270/245 is 2/3675
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 21,75,245 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,75,245) = 1
common factors(in case of two or more numbers have common factors) = 105
GCF(21,75,245) x common factors =1 x 105 = 105
LCM(21,75,245) = ( 21 × 75 × 245 ) / 105
LCM(21,75,245) = 385875 / 105
LCM(21,75,245) = 3675
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 64,192,270?
The HCF of 64,192,270 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 64/21, 192/75, 270/245?
Answer: GCF of Numerators as per given numbers 64/21, 192/75, 270/245 is
GCF of Numerators i.e. for 64,192,270 is 2
LCM of denominators i.e. for 21,75,245 is 3675.
Thus, GCF of Fractions is 2/3675.Finally, GCF of Fractions for 64/21, 192/75, 270/245 is 2/3675.