Use our free GCF of Fractions Calculator tool to compute the GCF of 21/40, 27/648, 242/241 i.e 1/780840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/40, 27/648, 242/241.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 21/40,27/648,242/241
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 21/40,27/648,242/241, numerators are 21,27,242
Denominators are 40,648,241
The GCF of 21,27,242 is 1 .
LCM of 40,648,241 is 780840.
The greatest common factor of 21/40,27/648,242/241 = [GCF of 21,27,242]/[LCM of 40,648,241]= 1/780840
Therefore, the GCF of 21/40,27/648,242/241 is 1/780840.
To find the highest common factor of 21,27,242, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 27 are 1, 3, 9, 27
The factors of 242 are 1, 2, 11, 22, 121, 242
The HCF of 21,27,242 is 1.
Lets's calculate GCF of 21,27,242
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 242
:1,2,11,22,121,242
Greatest Common Factor
We found the factors 21,27,242 . The biggest common factor number is the GCF number.
So the greatest common factor 21,27,242 is 1.
Lets's calculate LCM of 40,648,241
2 | 40, 648, 241 |
2 | 20, 324, 241 |
2 | 10, 162, 241 |
5, 81, 241 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 81 x 241 = 780840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/780840
Therefore, the GCF of Fractions 21/40,27/648,242/241 is 1/780840
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 40,648,241 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,648,241) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(40,648,241) x common factors =1 x 8 = 8
LCM(40,648,241) = ( 40 × 648 × 241 ) / 8
LCM(40,648,241) = 6246720 / 8
LCM(40,648,241) = 780840
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 21,27,242?
The HCF of 21,27,242 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 21/40, 27/648, 242/241?
Answer: GCF of Numerators as per given numbers 21/40, 27/648, 242/241 is
GCF of Numerators i.e. for 21,27,242 is 1
LCM of denominators i.e. for 40,648,241 is 780840.
Thus, GCF of Fractions is 1/780840.Finally, GCF of Fractions for 21/40, 27/648, 242/241 is 1/780840.