Use our free GCF of Fractions Calculator tool to compute the GCF of 270/446, 765/386 i.e 45/86078 easily. The following is the detailed procedure to determine the greatest common factor of fractions 270/446, 765/386.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 270/446,765/386
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 270/446,765/386, numerators are 270,765
Denominators are 446,386
The GCF of 270,765 is 45 .
LCM of 446,386 is 86078.
The greatest common factor of 270/446,765/386 = [GCF of 270,765]/[LCM of 446,386]= 45/86078
Therefore, the GCF of 270/446,765/386 is 45/86078.
To find the highest common factor of 270,765, we have to find the factors of both numbers and list the highest common factor.
The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The HCF of 270,765 is 45.
Lets's calculate GCF of 270,765
3 | 270, 765 |
3 | 90, 255 |
5 | 30, 85 |
6, 17 |
∴ So the GCF of the given numbers is 3 x 3 x 5 = 45
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 765
:1,3,5,9,15,17,45,51,85,153,255,765
Greatest Common Factor
We found the factors 270,765 . The biggest common factor number is the GCF number.
So the greatest common factor 270,765 is 45.
Lets's calculate LCM of 446,386
2 | 446, 386 |
223, 193 |
∴ So the LCM of the given numbers is 2 x 223 x 193 = 86078
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/86078
Therefore, the GCF of Fractions 270/446,765/386 is 45/86078
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 446,386 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(446,386) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(446,386) x common factors =2 x 1 = 2
LCM(446,386) = ( 446 × 386 ) / 2
LCM(446,386) = 172156 / 2
LCM(446,386) = 86078
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 270,765?
The HCF of 270,765 is 45
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 270/446, 765/386?
Answer: GCF of Numerators as per given numbers 270/446, 765/386 is
GCF of Numerators i.e. for 270,765 is 45
LCM of denominators i.e. for 446,386 is 86078.
Thus, GCF of Fractions is 45/86078.Finally, GCF of Fractions for 270/446, 765/386 is 45/86078.