GCF of 343/54, 666/49, 198/18
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 343/54, 666/49, 198/18 i.e 1/2646 easily. The following is the detailed procedure to determine the greatest common factor of fractions 343/54, 666/49, 198/18.
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 343/54,666/49,198/18?
Given fractions are 343/54,666/49,198/18
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 343/54,666/49,198/18, numerators are 343,666,198
Denominators are 54,49,18
The GCF of 343,666,198 is 1 .
LCM of 54,49,18 is 2646.
The greatest common factor of 343/54,666/49,198/18 = [GCF of 343,666,198]/[LCM of 54,49,18]= 1/2646
Therefore, the GCF of 343/54,666/49,198/18 is 1/2646.
To find the highest common factor of 343,666,198, we have to find the factors of both numbers and list the highest common factor.
The factors of 343 are 1, 7, 49, 343
The factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The HCF of 343,666,198 is 1.
Lets's calculate GCF of 343,666,198
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 343,666,198 By Matching Biggest Common Factor Method
Now, list down the factors of 343
:1,7,49,343
Now, list down the factors of 666
:1,2,3,6,9,18,37,74,111,222,333,666
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Greatest Common Factor
We found the factors 343,666,198 . The biggest common factor number is the GCF number.
So the greatest common factor 343,666,198 is 1.
Lets's calculate LCM of 54,49,18
| 2 | 54, 49, 18 |
| 3 | 27, 49, 9 |
| 3 | 3, 49, 9 |
| 1, 49, 3 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 1 x 49 x 3 = 2646
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2646
Therefore, the GCF of Fractions 343/54,666/49,198/18 is 1/2646
Least Common Multiple of 54,49,18 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 54,49,18 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,49,18) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(54,49,18) x common factors =1 x 18 = 18
LCM(54,49,18) = ( 54 × 49 × 18 ) / 18
LCM(54,49,18) = 47628 / 18
LCM(54,49,18) = 2646
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FAQs on GCF of Fractions of 343/54, 666/49, 198/18
1. What is the HCF of 343,666,198?
The HCF of 343,666,198 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 343/54, 666/49, 198/18?
Answer: GCF of Numerators as per given numbers 343/54, 666/49, 198/18 is
GCF of Numerators i.e. for 343,666,198 is 1
LCM of denominators i.e. for 54,49,18 is 2646.
Thus, GCF of Fractions is 1/2646.Finally, GCF of Fractions for 343/54, 666/49, 198/18 is 1/2646.