Use our free GCF of Fractions Calculator tool to compute the GCF of 142/309, 568/294 i.e 142/30282 easily. The following is the detailed procedure to determine the greatest common factor of fractions 142/309, 568/294.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 142/309,568/294
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 142/309,568/294, numerators are 142,568
Denominators are 309,294
The GCF of 142,568 is 142 .
LCM of 309,294 is 30282.
The greatest common factor of 142/309,568/294 = [GCF of 142,568]/[LCM of 309,294]= 142/30282
Therefore, the GCF of 142/309,568/294 is 142/30282.
To find the highest common factor of 142,568, we have to find the factors of both numbers and list the highest common factor.
The factors of 142 are 1, 2, 71, 142
The factors of 568 are 1, 2, 4, 8, 71, 142, 284, 568
The HCF of 142,568 is 142.
Lets's calculate GCF of 142,568
2 | 142, 568 |
71 | 71, 284 |
1, 4 |
∴ So the GCF of the given numbers is 2 x 71 = 142
Now, list down the factors of 142
:1,2,71,142
Now, list down the factors of 568
:1,2,4,8,71,142,284,568
Greatest Common Factor
We found the factors 142,568 . The biggest common factor number is the GCF number.
So the greatest common factor 142,568 is 142.
Lets's calculate LCM of 309,294
3 | 309, 294 |
103, 98 |
∴ So the LCM of the given numbers is 3 x 103 x 98 = 30282
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 142/30282
Therefore, the GCF of Fractions 142/309,568/294 is 142/30282
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 309,294 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,294) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(309,294) x common factors =3 x 1 = 3
LCM(309,294) = ( 309 × 294 ) / 3
LCM(309,294) = 90846 / 3
LCM(309,294) = 30282
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 142,568?
The HCF of 142,568 is 142
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 142/309, 568/294?
Answer: GCF of Numerators as per given numbers 142/309, 568/294 is
GCF of Numerators i.e. for 142,568 is 142
LCM of denominators i.e. for 309,294 is 30282.
Thus, GCF of Fractions is 142/30282.Finally, GCF of Fractions for 142/309, 568/294 is 142/30282.