GCF of 542/31, 649/673
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 542/31, 649/673 i.e 1/20863 easily. The following is the detailed procedure to determine the greatest common factor of fractions 542/31, 649/673.
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 542/31,649/673?
Given fractions are 542/31,649/673
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 542/31,649/673, numerators are 542,649
Denominators are 31,673
The GCF of 542,649 is 1 .
LCM of 31,673 is 20863.
The greatest common factor of 542/31,649/673 = [GCF of 542,649]/[LCM of 31,673]= 1/20863
Therefore, the GCF of 542/31,649/673 is 1/20863.
To find the highest common factor of 542,649, 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 649 are 1, 11, 59, 649
The HCF of 542,649 is 1.
Lets's calculate GCF of 542,649
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 542,649 By Matching Biggest Common Factor Method
Now, list down the factors of 542
:1,2,271,542
Now, list down the factors of 649
:1,11,59,649
Greatest Common Factor
We found the factors 542,649 . The biggest common factor number is the GCF number.
So the greatest common factor 542,649 is 1.
Lets's calculate LCM of 31,673
Given numbers has no common factors except 1. So, there LCM is their product i.e 20863
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/20863
Therefore, the GCF of Fractions 542/31,649/673 is 1/20863
Least Common Multiple of 31,673 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 31,673 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,673) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,673) x common factors =1 x 1 = 1
LCM(31,673) = ( 31 × 673 ) / 1
LCM(31,673) = 20863 / 1
LCM(31,673) = 20863
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FAQs on GCF of Fractions of 542/31, 649/673
1. What is the HCF of 542,649?
The HCF of 542,649 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 542/31, 649/673?
Answer: GCF of Numerators as per given numbers 542/31, 649/673 is
GCF of Numerators i.e. for 542,649 is 1
LCM of denominators i.e. for 31,673 is 20863.
Thus, GCF of Fractions is 1/20863.Finally, GCF of Fractions for 542/31, 649/673 is 1/20863.