Use our free GCF of Fractions Calculator tool to compute the GCF of 270/430, 786/336 i.e 6/72240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 270/430, 786/336.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 270/430,786/336
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 270/430,786/336, numerators are 270,786
Denominators are 430,336
The GCF of 270,786 is 6 .
LCM of 430,336 is 72240.
The greatest common factor of 270/430,786/336 = [GCF of 270,786]/[LCM of 430,336]= 6/72240
Therefore, the GCF of 270/430,786/336 is 6/72240.
To find the highest common factor of 270,786, 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 786 are 1, 2, 3, 6, 131, 262, 393, 786
The HCF of 270,786 is 6.
Lets's calculate GCF of 270,786
2 | 270, 786 |
3 | 135, 393 |
45, 131 |
∴ So the GCF of the given numbers is 2 x 3 = 6
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 786
:1,2,3,6,131,262,393,786
Greatest Common Factor
We found the factors 270,786 . The biggest common factor number is the GCF number.
So the greatest common factor 270,786 is 6.
Lets's calculate LCM of 430,336
2 | 430, 336 |
215, 168 |
∴ So the LCM of the given numbers is 2 x 215 x 168 = 72240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/72240
Therefore, the GCF of Fractions 270/430,786/336 is 6/72240
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 430,336 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(430,336) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(430,336) x common factors =2 x 1 = 2
LCM(430,336) = ( 430 × 336 ) / 2
LCM(430,336) = 144480 / 2
LCM(430,336) = 72240
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 270,786?
The HCF of 270,786 is 6
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 270/430, 786/336?
Answer: GCF of Numerators as per given numbers 270/430, 786/336 is
GCF of Numerators i.e. for 270,786 is 6
LCM of denominators i.e. for 430,336 is 72240.
Thus, GCF of Fractions is 6/72240.Finally, GCF of Fractions for 270/430, 786/336 is 6/72240.