GCF of 213/409, 317/993
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 213/409, 317/993 i.e 1/406137 easily. The following is the detailed procedure to determine the greatest common factor of fractions 213/409, 317/993.
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 213/409,317/993?
Given fractions are 213/409,317/993
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 213/409,317/993, numerators are 213,317
Denominators are 409,993
The GCF of 213,317 is 1 .
LCM of 409,993 is 406137.
The greatest common factor of 213/409,317/993 = [GCF of 213,317]/[LCM of 409,993]= 1/406137
Therefore, the GCF of 213/409,317/993 is 1/406137.
To find the highest common factor of 213,317, we have to find the factors of both numbers and list the highest common factor.
The factors of 213 are 1, 3, 71, 213
The factors of 317 are 1, 317
The HCF of 213,317 is 1.
Lets's calculate GCF of 213,317
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 213,317 By Matching Biggest Common Factor Method
Now, list down the factors of 213
:1,3,71,213
Now, list down the factors of 317
:1,317
Greatest Common Factor
We found the factors 213,317 . The biggest common factor number is the GCF number.
So the greatest common factor 213,317 is 1.
Lets's calculate LCM of 409,993
Given numbers has no common factors except 1. So, there LCM is their product i.e 406137
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/406137
Therefore, the GCF of Fractions 213/409,317/993 is 1/406137
Least Common Multiple of 409,993 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 409,993 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,993) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,993) x common factors =1 x 1 = 1
LCM(409,993) = ( 409 × 993 ) / 1
LCM(409,993) = 406137 / 1
LCM(409,993) = 406137
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 213/409, 317/993
1. What is the HCF of 213,317?
The HCF of 213,317 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 213/409, 317/993?
Answer: GCF of Numerators as per given numbers 213/409, 317/993 is
GCF of Numerators i.e. for 213,317 is 1
LCM of denominators i.e. for 409,993 is 406137.
Thus, GCF of Fractions is 1/406137.Finally, GCF of Fractions for 213/409, 317/993 is 1/406137.