Use our free GCF of Fractions Calculator tool to compute the GCF of 486/653, 342/766 i.e 18/500198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 486/653, 342/766.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 486/653,342/766
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 486/653,342/766, numerators are 486,342
Denominators are 653,766
The GCF of 486,342 is 18 .
LCM of 653,766 is 500198.
The greatest common factor of 486/653,342/766 = [GCF of 486,342]/[LCM of 653,766]= 18/500198
Therefore, the GCF of 486/653,342/766 is 18/500198.
To find the highest common factor of 486,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 486 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 486,342 is 18.
Lets's calculate GCF of 486,342
2 | 486, 342 |
3 | 243, 171 |
3 | 81, 57 |
27, 19 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Now, list down the factors of 486
:1,2,3,6,9,18,27,54,81,162,243,486
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 486,342 . The biggest common factor number is the GCF number.
So the greatest common factor 486,342 is 18.
Lets's calculate LCM of 653,766
Given numbers has no common factors except 1. So, there LCM is their product i.e 500198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/500198
Therefore, the GCF of Fractions 486/653,342/766 is 18/500198
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 653,766 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(653,766) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(653,766) x common factors =1 x 1 = 1
LCM(653,766) = ( 653 × 766 ) / 1
LCM(653,766) = 500198 / 1
LCM(653,766) = 500198
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 486,342?
The HCF of 486,342 is 18
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 486/653, 342/766?
Answer: GCF of Numerators as per given numbers 486/653, 342/766 is
GCF of Numerators i.e. for 486,342 is 18
LCM of denominators i.e. for 653,766 is 500198.
Thus, GCF of Fractions is 18/500198.Finally, GCF of Fractions for 486/653, 342/766 is 18/500198.