Use our free GCF of Fractions Calculator tool to compute the GCF of 56/60, 270/20, 405/147 i.e 1/2940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 56/60, 270/20, 405/147.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 56/60,270/20,405/147
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 56/60,270/20,405/147, numerators are 56,270,405
Denominators are 60,20,147
The GCF of 56,270,405 is 1 .
LCM of 60,20,147 is 2940.
The greatest common factor of 56/60,270/20,405/147 = [GCF of 56,270,405]/[LCM of 60,20,147]= 1/2940
Therefore, the GCF of 56/60,270/20,405/147 is 1/2940.
To find the highest common factor of 56,270,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 56,270,405 is 1.
Lets's calculate GCF of 56,270,405
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 56
:1,2,4,7,8,14,28,56
Now, list down the factors of 270
:1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 56,270,405 . The biggest common factor number is the GCF number.
So the greatest common factor 56,270,405 is 1.
Lets's calculate LCM of 60,20,147
2 | 60, 20, 147 |
2 | 30, 10, 147 |
3 | 15, 5, 147 |
5 | 5, 5, 49 |
1, 1, 49 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 1 x 49 = 2940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2940
Therefore, the GCF of Fractions 56/60,270/20,405/147 is 1/2940
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 60,20,147 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,20,147) = 1
common factors(in case of two or more numbers have common factors) = 60
GCF(60,20,147) x common factors =1 x 60 = 60
LCM(60,20,147) = ( 60 × 20 × 147 ) / 60
LCM(60,20,147) = 176400 / 60
LCM(60,20,147) = 2940
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 56,270,405?
The HCF of 56,270,405 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 56/60, 270/20, 405/147?
Answer: GCF of Numerators as per given numbers 56/60, 270/20, 405/147 is
GCF of Numerators i.e. for 56,270,405 is 1
LCM of denominators i.e. for 60,20,147 is 2940.
Thus, GCF of Fractions is 1/2940.Finally, GCF of Fractions for 56/60, 270/20, 405/147 is 1/2940.