Use our free GCF of Fractions Calculator tool to compute the GCF of 205/121, 542/506 i.e 1/5566 easily. The following is the detailed procedure to determine the greatest common factor of fractions 205/121, 542/506.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 205/121,542/506
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 205/121,542/506, numerators are 205,542
Denominators are 121,506
The GCF of 205,542 is 1 .
LCM of 121,506 is 5566.
The greatest common factor of 205/121,542/506 = [GCF of 205,542]/[LCM of 121,506]= 1/5566
Therefore, the GCF of 205/121,542/506 is 1/5566.
To find the highest common factor of 205,542, we have to find the factors of both numbers and list the highest common factor.
The factors of 205 are 1, 5, 41, 205
The factors of 542 are 1, 2, 271, 542
The HCF of 205,542 is 1.
Lets's calculate GCF of 205,542
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 205
:1,5,41,205
Now, list down the factors of 542
:1,2,271,542
Greatest Common Factor
We found the factors 205,542 . The biggest common factor number is the GCF number.
So the greatest common factor 205,542 is 1.
Lets's calculate LCM of 121,506
11 | 121, 506 |
11, 46 |
∴ So the LCM of the given numbers is 11 x 11 x 46 = 5566
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5566
Therefore, the GCF of Fractions 205/121,542/506 is 1/5566
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 121,506 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(121,506) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(121,506) x common factors =11 x 1 = 11
LCM(121,506) = ( 121 × 506 ) / 11
LCM(121,506) = 61226 / 11
LCM(121,506) = 5566
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 205,542?
The HCF of 205,542 is 1
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 205/121, 542/506?
Answer: GCF of Numerators as per given numbers 205/121, 542/506 is
GCF of Numerators i.e. for 205,542 is 1
LCM of denominators i.e. for 121,506 is 5566.
Thus, GCF of Fractions is 1/5566.Finally, GCF of Fractions for 205/121, 542/506 is 1/5566.