Use our free GCF of Fractions Calculator tool to compute the GCF of 542/306, 182/261 i.e 2/8874 easily. The following is the detailed procedure to determine the greatest common factor of fractions 542/306, 182/261.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 542/306,182/261
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 542/306,182/261, numerators are 542,182
Denominators are 306,261
The GCF of 542,182 is 2 .
LCM of 306,261 is 8874.
The greatest common factor of 542/306,182/261 = [GCF of 542,182]/[LCM of 306,261]= 2/8874
Therefore, the GCF of 542/306,182/261 is 2/8874.
To find the highest common factor of 542,182, we have to find the factors of both numbers and list the highest common factor.
The factors of 542 are 1, 2, 271, 542
The factors of 182 are 1, 2, 7, 13, 14, 26, 91, 182
The HCF of 542,182 is 2.
Lets's calculate GCF of 542,182
2 | 542, 182 |
271, 91 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 542
:1,2,271,542
Now, list down the factors of 182
:1,2,7,13,14,26,91,182
Greatest Common Factor
We found the factors 542,182 . The biggest common factor number is the GCF number.
So the greatest common factor 542,182 is 2.
Lets's calculate LCM of 306,261
3 | 306, 261 |
3 | 102, 87 |
34, 29 |
∴ So the LCM of the given numbers is 3 x 3 x 34 x 29 = 8874
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/8874
Therefore, the GCF of Fractions 542/306,182/261 is 2/8874
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 306,261 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(306,261) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(306,261) x common factors =9 x 1 = 9
LCM(306,261) = ( 306 × 261 ) / 9
LCM(306,261) = 79866 / 9
LCM(306,261) = 8874
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 542,182?
The HCF of 542,182 is 2
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 542/306, 182/261?
Answer: GCF of Numerators as per given numbers 542/306, 182/261 is
GCF of Numerators i.e. for 542,182 is 2
LCM of denominators i.e. for 306,261 is 8874.
Thus, GCF of Fractions is 2/8874.Finally, GCF of Fractions for 542/306, 182/261 is 2/8874.