Use our free GCF of Fractions Calculator tool to compute the GCF of 512/514, 542/535 i.e 2/274990 easily. The following is the detailed procedure to determine the greatest common factor of fractions 512/514, 542/535.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 512/514,542/535
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 512/514,542/535, numerators are 512,542
Denominators are 514,535
The GCF of 512,542 is 2 .
LCM of 514,535 is 274990.
The greatest common factor of 512/514,542/535 = [GCF of 512,542]/[LCM of 514,535]= 2/274990
Therefore, the GCF of 512/514,542/535 is 2/274990.
To find the highest common factor of 512,542, we have to find the factors of both numbers and list the highest common factor.
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The factors of 542 are 1, 2, 271, 542
The HCF of 512,542 is 2.
Lets's calculate GCF of 512,542
2 | 512, 542 |
256, 271 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Now, list down the factors of 542
:1,2,271,542
Greatest Common Factor
We found the factors 512,542 . The biggest common factor number is the GCF number.
So the greatest common factor 512,542 is 2.
Lets's calculate LCM of 514,535
Given numbers has no common factors except 1. So, there LCM is their product i.e 274990
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/274990
Therefore, the GCF of Fractions 512/514,542/535 is 2/274990
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 514,535 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(514,535) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(514,535) x common factors =1 x 1 = 1
LCM(514,535) = ( 514 × 535 ) / 1
LCM(514,535) = 274990 / 1
LCM(514,535) = 274990
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 512,542?
The HCF of 512,542 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 512/514, 542/535?
Answer: GCF of Numerators as per given numbers 512/514, 542/535 is
GCF of Numerators i.e. for 512,542 is 2
LCM of denominators i.e. for 514,535 is 274990.
Thus, GCF of Fractions is 2/274990.Finally, GCF of Fractions for 512/514, 542/535 is 2/274990.