GCF of 501/588, 138/542
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 501/588, 138/542 i.e 3/159348 easily. The following is the detailed procedure to determine the greatest common factor of fractions 501/588, 138/542.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 501/588,138/542?
Given fractions are 501/588,138/542
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 501/588,138/542, numerators are 501,138
Denominators are 588,542
The GCF of 501,138 is 3 .
LCM of 588,542 is 159348.
The greatest common factor of 501/588,138/542 = [GCF of 501,138]/[LCM of 588,542]= 3/159348
Therefore, the GCF of 501/588,138/542 is 3/159348.
To find the highest common factor of 501,138, we have to find the factors of both numbers and list the highest common factor.
The factors of 501 are 1, 3, 167, 501
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The HCF of 501,138 is 3.
Lets's calculate GCF of 501,138
| 3 | 501, 138 |
| 167, 46 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 501,138 By Matching Biggest Common Factor Method
Now, list down the factors of 501
:1,3,167,501
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Greatest Common Factor
We found the factors 501,138 . The biggest common factor number is the GCF number.
So the greatest common factor 501,138 is 3.
Lets's calculate LCM of 588,542
| 2 | 588, 542 |
| 294, 271 |
∴ So the LCM of the given numbers is 2 x 294 x 271 = 159348
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/159348
Therefore, the GCF of Fractions 501/588,138/542 is 3/159348
Least Common Multiple of 588,542 with GCF Formula
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 588,542 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(588,542) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(588,542) x common factors =2 x 1 = 2
LCM(588,542) = ( 588 × 542 ) / 2
LCM(588,542) = 318696 / 2
LCM(588,542) = 159348
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FAQs on GCF of Fractions of 501/588, 138/542
1. What is the HCF of 501,138?
The HCF of 501,138 is 3
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 501/588, 138/542?
Answer: GCF of Numerators as per given numbers 501/588, 138/542 is
GCF of Numerators i.e. for 501,138 is 3
LCM of denominators i.e. for 588,542 is 159348.
Thus, GCF of Fractions is 3/159348.Finally, GCF of Fractions for 501/588, 138/542 is 3/159348.