GCF of 82/413, 57/288, 217/643
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 82/413, 57/288, 217/643 i.e 1/76480992 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/413, 57/288, 217/643.
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 82/413,57/288,217/643?
Given fractions are 82/413,57/288,217/643
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 82/413,57/288,217/643, numerators are 82,57,217
Denominators are 413,288,643
The GCF of 82,57,217 is 1 .
LCM of 413,288,643 is 76480992.
The greatest common factor of 82/413,57/288,217/643 = [GCF of 82,57,217]/[LCM of 413,288,643]= 1/76480992
Therefore, the GCF of 82/413,57/288,217/643 is 1/76480992.
To find the highest common factor of 82,57,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 82 are 1, 2, 41, 82
The factors of 57 are 1, 3, 19, 57
The factors of 217 are 1, 7, 31, 217
The HCF of 82,57,217 is 1.
Lets's calculate GCF of 82,57,217
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 82,57,217 By Matching Biggest Common Factor Method
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 57
:1,3,19,57
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 82,57,217 . The biggest common factor number is the GCF number.
So the greatest common factor 82,57,217 is 1.
Lets's calculate LCM of 413,288,643
Given numbers has no common factors except 1. So, there LCM is their product i.e 76480992
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/76480992
Therefore, the GCF of Fractions 82/413,57/288,217/643 is 1/76480992
Least Common Multiple of 413,288,643 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 413,288,643 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(413,288,643) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(413,288,643) x common factors =1 x 1 = 1
LCM(413,288,643) = ( 413 × 288 × 643 ) / 1
LCM(413,288,643) = 76480992 / 1
LCM(413,288,643) = 76480992
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FAQs on GCF of Fractions of 82/413, 57/288, 217/643
1. What is the HCF of 82,57,217?
The HCF of 82,57,217 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 82/413, 57/288, 217/643?
Answer: GCF of Numerators as per given numbers 82/413, 57/288, 217/643 is
GCF of Numerators i.e. for 82,57,217 is 1
LCM of denominators i.e. for 413,288,643 is 76480992.
Thus, GCF of Fractions is 1/76480992.Finally, GCF of Fractions for 82/413, 57/288, 217/643 is 1/76480992.