GCF of 217/82, 405/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 217/82, 405/214 i.e 1/8774 easily. The following is the detailed procedure to determine the greatest common factor of fractions 217/82, 405/214.
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 217/82,405/214?
Given fractions are 217/82,405/214
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 217/82,405/214, numerators are 217,405
Denominators are 82,214
The GCF of 217,405 is 1 .
LCM of 82,214 is 8774.
The greatest common factor of 217/82,405/214 = [GCF of 217,405]/[LCM of 82,214]= 1/8774
Therefore, the GCF of 217/82,405/214 is 1/8774.
To find the highest common factor of 217,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 217 are 1, 7, 31, 217
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 217,405 is 1.
Lets's calculate GCF of 217,405
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 217,405 By Matching Biggest Common Factor Method
Now, list down the factors of 217
:1,7,31,217
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 217,405 . The biggest common factor number is the GCF number.
So the greatest common factor 217,405 is 1.
Lets's calculate LCM of 82,214
| 2 | 82, 214 |
| 41, 107 |
∴ So the LCM of the given numbers is 2 x 41 x 107 = 8774
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8774
Therefore, the GCF of Fractions 217/82,405/214 is 1/8774
Least Common Multiple of 82,214 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 82,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(82,214) x common factors =2 x 1 = 2
LCM(82,214) = ( 82 × 214 ) / 2
LCM(82,214) = 17548 / 2
LCM(82,214) = 8774
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FAQs on GCF of Fractions of 217/82, 405/214
1. What is the HCF of 217,405?
The HCF of 217,405 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 217/82, 405/214?
Answer: GCF of Numerators as per given numbers 217/82, 405/214 is
GCF of Numerators i.e. for 217,405 is 1
LCM of denominators i.e. for 82,214 is 8774.
Thus, GCF of Fractions is 1/8774.Finally, GCF of Fractions for 217/82, 405/214 is 1/8774.