GCF of 543/199, 234/648, 408/296
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 543/199, 234/648, 408/296 i.e 3/4771224 easily. The following is the detailed procedure to determine the greatest common factor of fractions 543/199, 234/648, 408/296.
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 543/199,234/648,408/296?
Given fractions are 543/199,234/648,408/296
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 543/199,234/648,408/296, numerators are 543,234,408
Denominators are 199,648,296
The GCF of 543,234,408 is 3 .
LCM of 199,648,296 is 4771224.
The greatest common factor of 543/199,234/648,408/296 = [GCF of 543,234,408]/[LCM of 199,648,296]= 3/4771224
Therefore, the GCF of 543/199,234/648,408/296 is 3/4771224.
To find the highest common factor of 543,234,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 543 are 1, 3, 181, 543
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 543,234,408 is 3.
Lets's calculate GCF of 543,234,408
| 3 | 543, 234, 408 |
| 181, 78, 136 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 543,234,408 By Matching Biggest Common Factor Method
Now, list down the factors of 543
:1,3,181,543
Now, list down the factors of 234
:1,2,3,6,9,13,18,26,39,78,117,234
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 543,234,408 . The biggest common factor number is the GCF number.
So the greatest common factor 543,234,408 is 3.
Lets's calculate LCM of 199,648,296
| 2 | 199, 648, 296 |
| 2 | 199, 324, 148 |
| 2 | 199, 162, 74 |
| 199, 81, 37 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 199 x 81 x 37 = 4771224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/4771224
Therefore, the GCF of Fractions 543/199,234/648,408/296 is 3/4771224
Least Common Multiple of 199,648,296 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 199,648,296 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(199,648,296) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(199,648,296) x common factors =1 x 8 = 8
LCM(199,648,296) = ( 199 × 648 × 296 ) / 8
LCM(199,648,296) = 38169792 / 8
LCM(199,648,296) = 4771224
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FAQs on GCF of Fractions of 543/199, 234/648, 408/296
1. What is the HCF of 543,234,408?
The HCF of 543,234,408 is 3
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 543/199, 234/648, 408/296?
Answer: GCF of Numerators as per given numbers 543/199, 234/648, 408/296 is
GCF of Numerators i.e. for 543,234,408 is 3
LCM of denominators i.e. for 199,648,296 is 4771224.
Thus, GCF of Fractions is 3/4771224.Finally, GCF of Fractions for 543/199, 234/648, 408/296 is 3/4771224.