GCF of 27/31, 343/38, 206/413
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 27/31, 343/38, 206/413 i.e 1/486514 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/31, 343/38, 206/413.
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 27/31,343/38,206/413?
Given fractions are 27/31,343/38,206/413
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 27/31,343/38,206/413, numerators are 27,343,206
Denominators are 31,38,413
The GCF of 27,343,206 is 1 .
LCM of 31,38,413 is 486514.
The greatest common factor of 27/31,343/38,206/413 = [GCF of 27,343,206]/[LCM of 31,38,413]= 1/486514
Therefore, the GCF of 27/31,343/38,206/413 is 1/486514.
To find the highest common factor of 27,343,206, we have to find the factors of both numbers and list the highest common factor.
The factors of 27 are 1, 3, 9, 27
The factors of 343 are 1, 7, 49, 343
The factors of 206 are 1, 2, 103, 206
The HCF of 27,343,206 is 1.
Lets's calculate GCF of 27,343,206
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 27,343,206 By Matching Biggest Common Factor Method
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 343
:1,7,49,343
Now, list down the factors of 206
:1,2,103,206
Greatest Common Factor
We found the factors 27,343,206 . The biggest common factor number is the GCF number.
So the greatest common factor 27,343,206 is 1.
Lets's calculate LCM of 31,38,413
Given numbers has no common factors except 1. So, there LCM is their product i.e 486514
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/486514
Therefore, the GCF of Fractions 27/31,343/38,206/413 is 1/486514
Least Common Multiple of 31,38,413 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 31,38,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,38,413) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,38,413) x common factors =1 x 1 = 1
LCM(31,38,413) = ( 31 × 38 × 413 ) / 1
LCM(31,38,413) = 486514 / 1
LCM(31,38,413) = 486514
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 27/31, 343/38, 206/413
1. What is the HCF of 27,343,206?
The HCF of 27,343,206 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 27/31, 343/38, 206/413?
Answer: GCF of Numerators as per given numbers 27/31, 343/38, 206/413 is
GCF of Numerators i.e. for 27,343,206 is 1
LCM of denominators i.e. for 31,38,413 is 486514.
Thus, GCF of Fractions is 1/486514.Finally, GCF of Fractions for 27/31, 343/38, 206/413 is 1/486514.