Use our free GCF of Fractions Calculator tool to compute the GCF of 300/286, 142/108 i.e 2/15444 easily. The following is the detailed procedure to determine the greatest common factor of fractions 300/286, 142/108.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 300/286,142/108
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 300/286,142/108, numerators are 300,142
Denominators are 286,108
The GCF of 300,142 is 2 .
LCM of 286,108 is 15444.
The greatest common factor of 300/286,142/108 = [GCF of 300,142]/[LCM of 286,108]= 2/15444
Therefore, the GCF of 300/286,142/108 is 2/15444.
To find the highest common factor of 300,142, we have to find the factors of both numbers and list the highest common factor.
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The factors of 142 are 1, 2, 71, 142
The HCF of 300,142 is 2.
Lets's calculate GCF of 300,142
2 | 300, 142 |
150, 71 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 300
:1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
Now, list down the factors of 142
:1,2,71,142
Greatest Common Factor
We found the factors 300,142 . The biggest common factor number is the GCF number.
So the greatest common factor 300,142 is 2.
Lets's calculate LCM of 286,108
2 | 286, 108 |
143, 54 |
∴ So the LCM of the given numbers is 2 x 143 x 54 = 15444
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/15444
Therefore, the GCF of Fractions 300/286,142/108 is 2/15444
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 286,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(286,108) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(286,108) x common factors =2 x 1 = 2
LCM(286,108) = ( 286 × 108 ) / 2
LCM(286,108) = 30888 / 2
LCM(286,108) = 15444
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 300,142?
The HCF of 300,142 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 300/286, 142/108?
Answer: GCF of Numerators as per given numbers 300/286, 142/108 is
GCF of Numerators i.e. for 300,142 is 2
LCM of denominators i.e. for 286,108 is 15444.
Thus, GCF of Fractions is 2/15444.Finally, GCF of Fractions for 300/286, 142/108 is 2/15444.