Use our free GCF of Fractions Calculator tool to compute the GCF of 540/606, 138/277 i.e 6/167862 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/606, 138/277.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 540/606,138/277
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 540/606,138/277, numerators are 540,138
Denominators are 606,277
The GCF of 540,138 is 6 .
LCM of 606,277 is 167862.
The greatest common factor of 540/606,138/277 = [GCF of 540,138]/[LCM of 606,277]= 6/167862
Therefore, the GCF of 540/606,138/277 is 6/167862.
To find the highest common factor of 540,138, we have to find the factors of both numbers and list the highest common factor.
The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The HCF of 540,138 is 6.
Lets's calculate GCF of 540,138
2 | 540, 138 |
3 | 270, 69 |
90, 23 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 540
:1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 540,138 . The biggest common factor number is the GCF number.
So the greatest common factor 540,138 is 6.
Lets's calculate LCM of 606,277
Given numbers has no common factors except 1. So, there LCM is their product i.e 167862
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/167862
Therefore, the GCF of Fractions 540/606,138/277 is 6/167862
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 606,277 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(606,277) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(606,277) x common factors =1 x 1 = 1
LCM(606,277) = ( 606 × 277 ) / 1
LCM(606,277) = 167862 / 1
LCM(606,277) = 167862
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 540,138?
The HCF of 540,138 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 540/606, 138/277?
Answer: GCF of Numerators as per given numbers 540/606, 138/277 is
GCF of Numerators i.e. for 540,138 is 6
LCM of denominators i.e. for 606,277 is 167862.
Thus, GCF of Fractions is 6/167862.Finally, GCF of Fractions for 540/606, 138/277 is 6/167862.