GCF of 578/243, 728/219
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 578/243, 728/219 i.e 2/17739 easily. The following is the detailed procedure to determine the greatest common factor of fractions 578/243, 728/219.
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 578/243,728/219?
Given fractions are 578/243,728/219
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 578/243,728/219, numerators are 578,728
Denominators are 243,219
The GCF of 578,728 is 2 .
LCM of 243,219 is 17739.
The greatest common factor of 578/243,728/219 = [GCF of 578,728]/[LCM of 243,219]= 2/17739
Therefore, the GCF of 578/243,728/219 is 2/17739.
To find the highest common factor of 578,728, we have to find the factors of both numbers and list the highest common factor.
The factors of 578 are 1, 2, 17, 34, 289, 578
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The HCF of 578,728 is 2.
Lets's calculate GCF of 578,728
| 2 | 578, 728 |
| 289, 364 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 578,728 By Matching Biggest Common Factor Method
Now, list down the factors of 578
:1,2,17,34,289,578
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 578,728 . The biggest common factor number is the GCF number.
So the greatest common factor 578,728 is 2.
Lets's calculate LCM of 243,219
| 3 | 243, 219 |
| 81, 73 |
∴ So the LCM of the given numbers is 3 x 81 x 73 = 17739
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/17739
Therefore, the GCF of Fractions 578/243,728/219 is 2/17739
Least Common Multiple of 243,219 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 243,219 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(243,219) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(243,219) x common factors =3 x 1 = 3
LCM(243,219) = ( 243 × 219 ) / 3
LCM(243,219) = 53217 / 3
LCM(243,219) = 17739
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FAQs on GCF of Fractions of 578/243, 728/219
1. What is the HCF of 578,728?
The HCF of 578,728 is 2
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 578/243, 728/219?
Answer: GCF of Numerators as per given numbers 578/243, 728/219 is
GCF of Numerators i.e. for 578,728 is 2
LCM of denominators i.e. for 243,219 is 17739.
Thus, GCF of Fractions is 2/17739.Finally, GCF of Fractions for 578/243, 728/219 is 2/17739.