GCF of 6740/105, 5617/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6740/105, 5617/814 i.e 1/85470 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6740/105, 5617/814.
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 6740/105,5617/814?
Given fractions are 6740/105,5617/814
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 6740/105,5617/814, numerators are 6740,5617
Denominators are 105,814
The GCF of 6740,5617 is 1 .
LCM of 105,814 is 85470.
The greatest common factor of 6740/105,5617/814 = [GCF of 6740,5617]/[LCM of 105,814]= 1/85470
Therefore, the GCF of 6740/105,5617/814 is 1/85470.
To find the highest common factor of 6740,5617, we have to find the factors of both numbers and list the highest common factor.
The factors of 6740 are 1, 2, 4, 5, 10, 20, 337, 674, 1348, 1685, 3370, 6740
The factors of 5617 are 1, 41, 137, 5617
The HCF of 6740,5617 is 1.
Lets's calculate GCF of 6740,5617
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 6740,5617 By Matching Biggest Common Factor Method
Now, list down the factors of 6740
:1,2,4,5,10,20,337,674,1348,1685,3370,6740
Now, list down the factors of 5617
:1,41,137,5617
Greatest Common Factor
We found the factors 6740,5617 . The biggest common factor number is the GCF number.
So the greatest common factor 6740,5617 is 1.
Lets's calculate LCM of 105,814
Given numbers has no common factors except 1. So, there LCM is their product i.e 85470
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/85470
Therefore, the GCF of Fractions 6740/105,5617/814 is 1/85470
Least Common Multiple of 105,814 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 105,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,814) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(105,814) x common factors =1 x 1 = 1
LCM(105,814) = ( 105 × 814 ) / 1
LCM(105,814) = 85470 / 1
LCM(105,814) = 85470
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FAQs on GCF of Fractions of 6740/105, 5617/814
1. What is the HCF of 6740,5617?
The HCF of 6740,5617 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 6740/105, 5617/814?
Answer: GCF of Numerators as per given numbers 6740/105, 5617/814 is
GCF of Numerators i.e. for 6740,5617 is 1
LCM of denominators i.e. for 105,814 is 85470.
Thus, GCF of Fractions is 1/85470.Finally, GCF of Fractions for 6740/105, 5617/814 is 1/85470.