GCF of 438/83, 219/173
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 438/83, 219/173 i.e 219/14359 easily. The following is the detailed procedure to determine the greatest common factor of fractions 438/83, 219/173.
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 438/83,219/173?
Given fractions are 438/83,219/173
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 438/83,219/173, numerators are 438,219
Denominators are 83,173
The GCF of 438,219 is 219 .
LCM of 83,173 is 14359.
The greatest common factor of 438/83,219/173 = [GCF of 438,219]/[LCM of 83,173]= 219/14359
Therefore, the GCF of 438/83,219/173 is 219/14359.
To find the highest common factor of 438,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438
The factors of 219 are 1, 3, 73, 219
The HCF of 438,219 is 219.
Lets's calculate GCF of 438,219
| 3 | 438, 219 |
| 73 | 146, 73 |
| 2, 1 |
∴ So the GCF of the given numbers is 3 x 73 = 219
Greatest Common Factor of 438,219 By Matching Biggest Common Factor Method
Now, list down the factors of 438
:1,2,3,6,73,146,219,438
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 438,219 . The biggest common factor number is the GCF number.
So the greatest common factor 438,219 is 219.
Lets's calculate LCM of 83,173
Given numbers has no common factors except 1. So, there LCM is their product i.e 14359
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 219/14359
Therefore, the GCF of Fractions 438/83,219/173 is 219/14359
Least Common Multiple of 83,173 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 83,173 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(83,173) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(83,173) x common factors =1 x 1 = 1
LCM(83,173) = ( 83 × 173 ) / 1
LCM(83,173) = 14359 / 1
LCM(83,173) = 14359
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FAQs on GCF of Fractions of 438/83, 219/173
1. What is the HCF of 438,219?
The HCF of 438,219 is 219
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 438/83, 219/173?
Answer: GCF of Numerators as per given numbers 438/83, 219/173 is
GCF of Numerators i.e. for 438,219 is 219
LCM of denominators i.e. for 83,173 is 14359.
Thus, GCF of Fractions is 219/14359.Finally, GCF of Fractions for 438/83, 219/173 is 219/14359.