Use our free GCF of Fractions Calculator tool to compute the GCF of 126/542, 810/468 i.e 18/126828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 126/542, 810/468.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 126/542,810/468
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 126/542,810/468, numerators are 126,810
Denominators are 542,468
The GCF of 126,810 is 18 .
LCM of 542,468 is 126828.
The greatest common factor of 126/542,810/468 = [GCF of 126,810]/[LCM of 542,468]= 18/126828
Therefore, the GCF of 126/542,810/468 is 18/126828.
To find the highest common factor of 126,810, we have to find the factors of both numbers and list the highest common factor.
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The HCF of 126,810 is 18.
Lets's calculate GCF of 126,810
2 | 126, 810 |
3 | 63, 405 |
3 | 21, 135 |
7, 45 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Now, list down the factors of 126
:1,2,3,6,7,9,14,18,21,42,63,126
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Greatest Common Factor
We found the factors 126,810 . The biggest common factor number is the GCF number.
So the greatest common factor 126,810 is 18.
Lets's calculate LCM of 542,468
2 | 542, 468 |
271, 234 |
∴ So the LCM of the given numbers is 2 x 271 x 234 = 126828
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/126828
Therefore, the GCF of Fractions 126/542,810/468 is 18/126828
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 542,468 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(542,468) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(542,468) x common factors =2 x 1 = 2
LCM(542,468) = ( 542 × 468 ) / 2
LCM(542,468) = 253656 / 2
LCM(542,468) = 126828
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 126,810?
The HCF of 126,810 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 126/542, 810/468?
Answer: GCF of Numerators as per given numbers 126/542, 810/468 is
GCF of Numerators i.e. for 126,810 is 18
LCM of denominators i.e. for 542,468 is 126828.
Thus, GCF of Fractions is 18/126828.Finally, GCF of Fractions for 126/542, 810/468 is 18/126828.