GCF of 271/31, 338/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 271/31, 338/419 i.e 1/12989 easily. The following is the detailed procedure to determine the greatest common factor of fractions 271/31, 338/419.
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 271/31,338/419?
Given fractions are 271/31,338/419
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 271/31,338/419, numerators are 271,338
Denominators are 31,419
The GCF of 271,338 is 1 .
LCM of 31,419 is 12989.
The greatest common factor of 271/31,338/419 = [GCF of 271,338]/[LCM of 31,419]= 1/12989
Therefore, the GCF of 271/31,338/419 is 1/12989.
To find the highest common factor of 271,338, we have to find the factors of both numbers and list the highest common factor.
The factors of 271 are 1, 271
The factors of 338 are 1, 2, 13, 26, 169, 338
The HCF of 271,338 is 1.
Lets's calculate GCF of 271,338
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 271,338 By Matching Biggest Common Factor Method
Now, list down the factors of 271
:1,271
Now, list down the factors of 338
:1,2,13,26,169,338
Greatest Common Factor
We found the factors 271,338 . The biggest common factor number is the GCF number.
So the greatest common factor 271,338 is 1.
Lets's calculate LCM of 31,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 12989
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12989
Therefore, the GCF of Fractions 271/31,338/419 is 1/12989
Least Common Multiple of 31,419 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 31,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,419) x common factors =1 x 1 = 1
LCM(31,419) = ( 31 × 419 ) / 1
LCM(31,419) = 12989 / 1
LCM(31,419) = 12989
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 271/31, 338/419
1. What is the HCF of 271,338?
The HCF of 271,338 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 271/31, 338/419?
Answer: GCF of Numerators as per given numbers 271/31, 338/419 is
GCF of Numerators i.e. for 271,338 is 1
LCM of denominators i.e. for 31,419 is 12989.
Thus, GCF of Fractions is 1/12989.Finally, GCF of Fractions for 271/31, 338/419 is 1/12989.