Use our free GCF of Fractions Calculator tool to compute the GCF of 294/312, 106/578 i.e 2/90168 easily. The following is the detailed procedure to determine the greatest common factor of fractions 294/312, 106/578.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 294/312,106/578
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 294/312,106/578, numerators are 294,106
Denominators are 312,578
The GCF of 294,106 is 2 .
LCM of 312,578 is 90168.
The greatest common factor of 294/312,106/578 = [GCF of 294,106]/[LCM of 312,578]= 2/90168
Therefore, the GCF of 294/312,106/578 is 2/90168.
To find the highest common factor of 294,106, we have to find the factors of both numbers and list the highest common factor.
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The factors of 106 are 1, 2, 53, 106
The HCF of 294,106 is 2.
Lets's calculate GCF of 294,106
2 | 294, 106 |
147, 53 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Now, list down the factors of 106
:1,2,53,106
Greatest Common Factor
We found the factors 294,106 . The biggest common factor number is the GCF number.
So the greatest common factor 294,106 is 2.
Lets's calculate LCM of 312,578
2 | 312, 578 |
156, 289 |
∴ So the LCM of the given numbers is 2 x 156 x 289 = 90168
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/90168
Therefore, the GCF of Fractions 294/312,106/578 is 2/90168
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 312,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,578) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(312,578) x common factors =2 x 1 = 2
LCM(312,578) = ( 312 × 578 ) / 2
LCM(312,578) = 180336 / 2
LCM(312,578) = 90168
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 294,106?
The HCF of 294,106 is 2
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 294/312, 106/578?
Answer: GCF of Numerators as per given numbers 294/312, 106/578 is
GCF of Numerators i.e. for 294,106 is 2
LCM of denominators i.e. for 312,578 is 90168.
Thus, GCF of Fractions is 2/90168.Finally, GCF of Fractions for 294/312, 106/578 is 2/90168.