GCF of 82/19, 64/91, 209/909
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 82/19, 64/91, 209/909 i.e 1/1571661 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/19, 64/91, 209/909.
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 82/19,64/91,209/909?
Given fractions are 82/19,64/91,209/909
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 82/19,64/91,209/909, numerators are 82,64,209
Denominators are 19,91,909
The GCF of 82,64,209 is 1 .
LCM of 19,91,909 is 1571661.
The greatest common factor of 82/19,64/91,209/909 = [GCF of 82,64,209]/[LCM of 19,91,909]= 1/1571661
Therefore, the GCF of 82/19,64/91,209/909 is 1/1571661.
To find the highest common factor of 82,64,209, 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 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 209 are 1, 11, 19, 209
The HCF of 82,64,209 is 1.
Lets's calculate GCF of 82,64,209
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 82,64,209 By Matching Biggest Common Factor Method
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 64
:1,2,4,8,16,32,64
Now, list down the factors of 209
:1,11,19,209
Greatest Common Factor
We found the factors 82,64,209 . The biggest common factor number is the GCF number.
So the greatest common factor 82,64,209 is 1.
Lets's calculate LCM of 19,91,909
Given numbers has no common factors except 1. So, there LCM is their product i.e 1571661
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1571661
Therefore, the GCF of Fractions 82/19,64/91,209/909 is 1/1571661
Least Common Multiple of 19,91,909 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 19,91,909 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(19,91,909) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(19,91,909) x common factors =1 x 1 = 1
LCM(19,91,909) = ( 19 × 91 × 909 ) / 1
LCM(19,91,909) = 1571661 / 1
LCM(19,91,909) = 1571661
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FAQs on GCF of Fractions of 82/19, 64/91, 209/909
1. What is the HCF of 82,64,209?
The HCF of 82,64,209 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 82/19, 64/91, 209/909?
Answer: GCF of Numerators as per given numbers 82/19, 64/91, 209/909 is
GCF of Numerators i.e. for 82,64,209 is 1
LCM of denominators i.e. for 19,91,909 is 1571661.
Thus, GCF of Fractions is 1/1571661.Finally, GCF of Fractions for 82/19, 64/91, 209/909 is 1/1571661.