GCF of 5230/339, 3430/105
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5230/339, 3430/105 i.e 10/11865 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5230/339, 3430/105.
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 5230/339,3430/105?
Given fractions are 5230/339,3430/105
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 5230/339,3430/105, numerators are 5230,3430
Denominators are 339,105
The GCF of 5230,3430 is 10 .
LCM of 339,105 is 11865.
The greatest common factor of 5230/339,3430/105 = [GCF of 5230,3430]/[LCM of 339,105]= 10/11865
Therefore, the GCF of 5230/339,3430/105 is 10/11865.
To find the highest common factor of 5230,3430, we have to find the factors of both numbers and list the highest common factor.
The factors of 5230 are 1, 2, 5, 10, 523, 1046, 2615, 5230
The factors of 3430 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 343, 490, 686, 1715, 3430
The HCF of 5230,3430 is 10.
Lets's calculate GCF of 5230,3430
| 2 | 5230, 3430 |
| 5 | 2615, 1715 |
| 523, 343 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 5230,3430 By Matching Biggest Common Factor Method
Now, list down the factors of 5230
:1,2,5,10,523,1046,2615,5230
Now, list down the factors of 3430
:1,2,5,7,10,14,35,49,70,98,245,343,490,686,1715,3430
Greatest Common Factor
We found the factors 5230,3430 . The biggest common factor number is the GCF number.
So the greatest common factor 5230,3430 is 10.
Lets's calculate LCM of 339,105
| 3 | 339, 105 |
| 113, 35 |
∴ So the LCM of the given numbers is 3 x 113 x 35 = 11865
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/11865
Therefore, the GCF of Fractions 5230/339,3430/105 is 10/11865
Least Common Multiple of 339,105 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 339,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(339,105) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(339,105) x common factors =3 x 1 = 3
LCM(339,105) = ( 339 × 105 ) / 3
LCM(339,105) = 35595 / 3
LCM(339,105) = 11865
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FAQs on GCF of Fractions of 5230/339, 3430/105
1. What is the HCF of 5230,3430?
The HCF of 5230,3430 is 10
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 5230/339, 3430/105?
Answer: GCF of Numerators as per given numbers 5230/339, 3430/105 is
GCF of Numerators i.e. for 5230,3430 is 10
LCM of denominators i.e. for 339,105 is 11865.
Thus, GCF of Fractions is 10/11865.Finally, GCF of Fractions for 5230/339, 3430/105 is 10/11865.