Use our free GCF of Fractions Calculator tool to compute the GCF of 87/309, 42/738, 270/671 i.e 3/51005394 easily. The following is the detailed procedure to determine the greatest common factor of fractions 87/309, 42/738, 270/671.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 87/309,42/738,270/671
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 87/309,42/738,270/671, numerators are 87,42,270
Denominators are 309,738,671
The GCF of 87,42,270 is 3 .
LCM of 309,738,671 is 51005394.
The greatest common factor of 87/309,42/738,270/671 = [GCF of 87,42,270]/[LCM of 309,738,671]= 3/51005394
Therefore, the GCF of 87/309,42/738,270/671 is 3/51005394.
To find the highest common factor of 87,42,270, we have to find the factors of both numbers and list the highest common factor.
The factors of 87 are 1, 3, 29, 87
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The HCF of 87,42,270 is 3.
Lets's calculate GCF of 87,42,270
3 | 87, 42, 270 |
29, 14, 90 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 87
:1,3,29,87
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
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 87,42,270 . The biggest common factor number is the GCF number.
So the greatest common factor 87,42,270 is 3.
Lets's calculate LCM of 309,738,671
3 | 309, 738, 671 |
103, 246, 671 |
∴ So the LCM of the given numbers is 3 x 103 x 246 x 671 = 51005394
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/51005394
Therefore, the GCF of Fractions 87/309,42/738,270/671 is 3/51005394
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 309,738,671 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,738,671) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(309,738,671) x common factors =1 x 3 = 3
LCM(309,738,671) = ( 309 × 738 × 671 ) / 3
LCM(309,738,671) = 153016182 / 3
LCM(309,738,671) = 51005394
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 87,42,270?
The HCF of 87,42,270 is 3
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 87/309, 42/738, 270/671?
Answer: GCF of Numerators as per given numbers 87/309, 42/738, 270/671 is
GCF of Numerators i.e. for 87,42,270 is 3
LCM of denominators i.e. for 309,738,671 is 51005394.
Thus, GCF of Fractions is 3/51005394.Finally, GCF of Fractions for 87/309, 42/738, 270/671 is 3/51005394.