GCF of 103/578, 214/339
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 103/578, 214/339 i.e 1/195942 easily. The following is the detailed procedure to determine the greatest common factor of fractions 103/578, 214/339.
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 103/578,214/339?
Given fractions are 103/578,214/339
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 103/578,214/339, numerators are 103,214
Denominators are 578,339
The GCF of 103,214 is 1 .
LCM of 578,339 is 195942.
The greatest common factor of 103/578,214/339 = [GCF of 103,214]/[LCM of 578,339]= 1/195942
Therefore, the GCF of 103/578,214/339 is 1/195942.
To find the highest common factor of 103,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 103 are 1, 103
The factors of 214 are 1, 2, 107, 214
The HCF of 103,214 is 1.
Lets's calculate GCF of 103,214
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 103,214 By Matching Biggest Common Factor Method
Now, list down the factors of 103
:1,103
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 103,214 . The biggest common factor number is the GCF number.
So the greatest common factor 103,214 is 1.
Lets's calculate LCM of 578,339
Given numbers has no common factors except 1. So, there LCM is their product i.e 195942
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/195942
Therefore, the GCF of Fractions 103/578,214/339 is 1/195942
Least Common Multiple of 578,339 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 578,339 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(578,339) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(578,339) x common factors =1 x 1 = 1
LCM(578,339) = ( 578 × 339 ) / 1
LCM(578,339) = 195942 / 1
LCM(578,339) = 195942
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 103/578, 214/339
1. What is the HCF of 103,214?
The HCF of 103,214 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 103/578, 214/339?
Answer: GCF of Numerators as per given numbers 103/578, 214/339 is
GCF of Numerators i.e. for 103,214 is 1
LCM of denominators i.e. for 578,339 is 195942.
Thus, GCF of Fractions is 1/195942.Finally, GCF of Fractions for 103/578, 214/339 is 1/195942.