Use our free GCF of Fractions Calculator tool to compute the GCF of 318/472, 300/828 i.e 6/97704 easily. The following is the detailed procedure to determine the greatest common factor of fractions 318/472, 300/828.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 318/472,300/828
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 318/472,300/828, numerators are 318,300
Denominators are 472,828
The GCF of 318,300 is 6 .
LCM of 472,828 is 97704.
The greatest common factor of 318/472,300/828 = [GCF of 318,300]/[LCM of 472,828]= 6/97704
Therefore, the GCF of 318/472,300/828 is 6/97704.
To find the highest common factor of 318,300, we have to find the factors of both numbers and list the highest common factor.
The factors of 318 are 1, 2, 3, 6, 53, 106, 159, 318
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The HCF of 318,300 is 6.
Lets's calculate GCF of 318,300
2 | 318, 300 |
3 | 159, 150 |
53, 50 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 318
:1,2,3,6,53,106,159,318
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
Greatest Common Factor
We found the factors 318,300 . The biggest common factor number is the GCF number.
So the greatest common factor 318,300 is 6.
Lets's calculate LCM of 472,828
2 | 472, 828 |
2 | 236, 414 |
118, 207 |
∴ So the LCM of the given numbers is 2 x 2 x 118 x 207 = 97704
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/97704
Therefore, the GCF of Fractions 318/472,300/828 is 6/97704
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 472,828 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(472,828) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(472,828) x common factors =4 x 1 = 4
LCM(472,828) = ( 472 × 828 ) / 4
LCM(472,828) = 390816 / 4
LCM(472,828) = 97704
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 318,300?
The HCF of 318,300 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 318/472, 300/828?
Answer: GCF of Numerators as per given numbers 318/472, 300/828 is
GCF of Numerators i.e. for 318,300 is 6
LCM of denominators i.e. for 472,828 is 97704.
Thus, GCF of Fractions is 6/97704.Finally, GCF of Fractions for 318/472, 300/828 is 6/97704.