GCF of 342/27, 219/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 342/27, 219/419 i.e 3/11313 easily. The following is the detailed procedure to determine the greatest common factor of fractions 342/27, 219/419.
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 342/27,219/419?
Given fractions are 342/27,219/419
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 342/27,219/419, numerators are 342,219
Denominators are 27,419
The GCF of 342,219 is 3 .
LCM of 27,419 is 11313.
The greatest common factor of 342/27,219/419 = [GCF of 342,219]/[LCM of 27,419]= 3/11313
Therefore, the GCF of 342/27,219/419 is 3/11313.
To find the highest common factor of 342,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The factors of 219 are 1, 3, 73, 219
The HCF of 342,219 is 3.
Lets's calculate GCF of 342,219
| 3 | 342, 219 |
| 114, 73 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 342,219 By Matching Biggest Common Factor Method
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 342,219 . The biggest common factor number is the GCF number.
So the greatest common factor 342,219 is 3.
Lets's calculate LCM of 27,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 11313
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/11313
Therefore, the GCF of Fractions 342/27,219/419 is 3/11313
Least Common Multiple of 27,419 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 27,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(27,419) x common factors =1 x 1 = 1
LCM(27,419) = ( 27 × 419 ) / 1
LCM(27,419) = 11313 / 1
LCM(27,419) = 11313
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FAQs on GCF of Fractions of 342/27, 219/419
1. What is the HCF of 342,219?
The HCF of 342,219 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 342/27, 219/419?
Answer: GCF of Numerators as per given numbers 342/27, 219/419 is
GCF of Numerators i.e. for 342,219 is 3
LCM of denominators i.e. for 27,419 is 11313.
Thus, GCF of Fractions is 3/11313.Finally, GCF of Fractions for 342/27, 219/419 is 3/11313.