Use our free GCF of Fractions Calculator tool to compute the GCF of 138/171, 759/729 i.e 69/13851 easily. The following is the detailed procedure to determine the greatest common factor of fractions 138/171, 759/729.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 138/171,759/729
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 138/171,759/729, numerators are 138,759
Denominators are 171,729
The GCF of 138,759 is 69 .
LCM of 171,729 is 13851.
The greatest common factor of 138/171,759/729 = [GCF of 138,759]/[LCM of 171,729]= 69/13851
Therefore, the GCF of 138/171,759/729 is 69/13851.
To find the highest common factor of 138,759, we have to find the factors of both numbers and list the highest common factor.
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The factors of 759 are 1, 3, 11, 23, 33, 69, 253, 759
The HCF of 138,759 is 69.
Lets's calculate GCF of 138,759
3 | 138, 759 |
23 | 46, 253 |
2, 11 |
∴ So the GCF of the given numbers is 3 x 23 = 69
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Now, list down the factors of 759
:1,3,11,23,33,69,253,759
Greatest Common Factor
We found the factors 138,759 . The biggest common factor number is the GCF number.
So the greatest common factor 138,759 is 69.
Lets's calculate LCM of 171,729
3 | 171, 729 |
3 | 57, 243 |
19, 81 |
∴ So the LCM of the given numbers is 3 x 3 x 19 x 81 = 13851
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 69/13851
Therefore, the GCF of Fractions 138/171,759/729 is 69/13851
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 171,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(171,729) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(171,729) x common factors =9 x 1 = 9
LCM(171,729) = ( 171 × 729 ) / 9
LCM(171,729) = 124659 / 9
LCM(171,729) = 13851
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 138,759?
The HCF of 138,759 is 69
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 138/171, 759/729?
Answer: GCF of Numerators as per given numbers 138/171, 759/729 is
GCF of Numerators i.e. for 138,759 is 69
LCM of denominators i.e. for 171,729 is 13851.
Thus, GCF of Fractions is 69/13851.Finally, GCF of Fractions for 138/171, 759/729 is 69/13851.