Use our free GCF of Fractions Calculator tool to compute the GCF of 243/445, 270/665 i.e 27/59185 easily. The following is the detailed procedure to determine the greatest common factor of fractions 243/445, 270/665.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 243/445,270/665
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 243/445,270/665, numerators are 243,270
Denominators are 445,665
The GCF of 243,270 is 27 .
LCM of 445,665 is 59185.
The greatest common factor of 243/445,270/665 = [GCF of 243,270]/[LCM of 445,665]= 27/59185
Therefore, the GCF of 243/445,270/665 is 27/59185.
To find the highest common factor of 243,270, we have to find the factors of both numbers and list the highest common factor.
The factors of 243 are 1, 3, 9, 27, 81, 243
The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The HCF of 243,270 is 27.
Lets's calculate GCF of 243,270
3 | 243, 270 |
3 | 81, 90 |
3 | 27, 30 |
9, 10 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Now, list down the factors of 243
:1,3,9,27,81,243
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 243,270 . The biggest common factor number is the GCF number.
So the greatest common factor 243,270 is 27.
Lets's calculate LCM of 445,665
5 | 445, 665 |
89, 133 |
∴ So the LCM of the given numbers is 5 x 89 x 133 = 59185
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/59185
Therefore, the GCF of Fractions 243/445,270/665 is 27/59185
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 445,665 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(445,665) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(445,665) x common factors =5 x 1 = 5
LCM(445,665) = ( 445 × 665 ) / 5
LCM(445,665) = 295925 / 5
LCM(445,665) = 59185
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 243,270?
The HCF of 243,270 is 27
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 243/445, 270/665?
Answer: GCF of Numerators as per given numbers 243/445, 270/665 is
GCF of Numerators i.e. for 243,270 is 27
LCM of denominators i.e. for 445,665 is 59185.
Thus, GCF of Fractions is 27/59185.Finally, GCF of Fractions for 243/445, 270/665 is 27/59185.