GCF of 9741/309, 6734/1646
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9741/309, 6734/1646 i.e 1/508614 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9741/309, 6734/1646.
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 9741/309,6734/1646?
Given fractions are 9741/309,6734/1646
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 9741/309,6734/1646, numerators are 9741,6734
Denominators are 309,1646
The GCF of 9741,6734 is 1 .
LCM of 309,1646 is 508614.
The greatest common factor of 9741/309,6734/1646 = [GCF of 9741,6734]/[LCM of 309,1646]= 1/508614
Therefore, the GCF of 9741/309,6734/1646 is 1/508614.
To find the highest common factor of 9741,6734, we have to find the factors of both numbers and list the highest common factor.
The factors of 9741 are 1, 3, 17, 51, 191, 573, 3247, 9741
The factors of 6734 are 1, 2, 7, 13, 14, 26, 37, 74, 91, 182, 259, 481, 518, 962, 3367, 6734
The HCF of 9741,6734 is 1.
Lets's calculate GCF of 9741,6734
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 9741,6734 By Matching Biggest Common Factor Method
Now, list down the factors of 9741
:1,3,17,51,191,573,3247,9741
Now, list down the factors of 6734
:1,2,7,13,14,26,37,74,91,182,259,481,518,962,3367,6734
Greatest Common Factor
We found the factors 9741,6734 . The biggest common factor number is the GCF number.
So the greatest common factor 9741,6734 is 1.
Lets's calculate LCM of 309,1646
Given numbers has no common factors except 1. So, there LCM is their product i.e 508614
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/508614
Therefore, the GCF of Fractions 9741/309,6734/1646 is 1/508614
Least Common Multiple of 309,1646 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 309,1646 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,1646) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(309,1646) x common factors =1 x 1 = 1
LCM(309,1646) = ( 309 × 1646 ) / 1
LCM(309,1646) = 508614 / 1
LCM(309,1646) = 508614
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FAQs on GCF of Fractions of 9741/309, 6734/1646
1. What is the HCF of 9741,6734?
The HCF of 9741,6734 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 9741/309, 6734/1646?
Answer: GCF of Numerators as per given numbers 9741/309, 6734/1646 is
GCF of Numerators i.e. for 9741,6734 is 1
LCM of denominators i.e. for 309,1646 is 508614.
Thus, GCF of Fractions is 1/508614.Finally, GCF of Fractions for 9741/309, 6734/1646 is 1/508614.