GCF of 259/334, 1306/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 259/334, 1306/419 i.e 1/139946 easily. The following is the detailed procedure to determine the greatest common factor of fractions 259/334, 1306/419.
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 259/334,1306/419?
Given fractions are 259/334,1306/419
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 259/334,1306/419, numerators are 259,1306
Denominators are 334,419
The GCF of 259,1306 is 1 .
LCM of 334,419 is 139946.
The greatest common factor of 259/334,1306/419 = [GCF of 259,1306]/[LCM of 334,419]= 1/139946
Therefore, the GCF of 259/334,1306/419 is 1/139946.
To find the highest common factor of 259,1306, we have to find the factors of both numbers and list the highest common factor.
The factors of 259 are 1, 7, 37, 259
The factors of 1306 are 1, 2, 653, 1306
The HCF of 259,1306 is 1.
Lets's calculate GCF of 259,1306
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 259,1306 By Matching Biggest Common Factor Method
Now, list down the factors of 259
:1,7,37,259
Now, list down the factors of 1306
:1,2,653,1306
Greatest Common Factor
We found the factors 259,1306 . The biggest common factor number is the GCF number.
So the greatest common factor 259,1306 is 1.
Lets's calculate LCM of 334,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 139946
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/139946
Therefore, the GCF of Fractions 259/334,1306/419 is 1/139946
Least Common Multiple of 334,419 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 334,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(334,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(334,419) x common factors =1 x 1 = 1
LCM(334,419) = ( 334 × 419 ) / 1
LCM(334,419) = 139946 / 1
LCM(334,419) = 139946
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FAQs on GCF of Fractions of 259/334, 1306/419
1. What is the HCF of 259,1306?
The HCF of 259,1306 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 259/334, 1306/419?
Answer: GCF of Numerators as per given numbers 259/334, 1306/419 is
GCF of Numerators i.e. for 259,1306 is 1
LCM of denominators i.e. for 334,419 is 139946.
Thus, GCF of Fractions is 1/139946.Finally, GCF of Fractions for 259/334, 1306/419 is 1/139946.