GCF of 6419/274, 3430/942
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6419/274, 3430/942 i.e 49/129054 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6419/274, 3430/942.
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 6419/274,3430/942?
Given fractions are 6419/274,3430/942
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 6419/274,3430/942, numerators are 6419,3430
Denominators are 274,942
The GCF of 6419,3430 is 49 .
LCM of 274,942 is 129054.
The greatest common factor of 6419/274,3430/942 = [GCF of 6419,3430]/[LCM of 274,942]= 49/129054
Therefore, the GCF of 6419/274,3430/942 is 49/129054.
To find the highest common factor of 6419,3430, we have to find the factors of both numbers and list the highest common factor.
The factors of 6419 are 1, 7, 49, 131, 917, 6419
The factors of 3430 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 343, 490, 686, 1715, 3430
The HCF of 6419,3430 is 49.
Lets's calculate GCF of 6419,3430
| 7 | 6419, 3430 |
| 7 | 917, 490 |
| 131, 70 |
∴ So the GCF of the given numbers is 7 x 7 = 49
Greatest Common Factor of 6419,3430 By Matching Biggest Common Factor Method
Now, list down the factors of 6419
:1,7,49,131,917,6419
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 6419,3430 . The biggest common factor number is the GCF number.
So the greatest common factor 6419,3430 is 49.
Lets's calculate LCM of 274,942
| 2 | 274, 942 |
| 137, 471 |
∴ So the LCM of the given numbers is 2 x 137 x 471 = 129054
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 49/129054
Therefore, the GCF of Fractions 6419/274,3430/942 is 49/129054
Least Common Multiple of 274,942 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 274,942 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(274,942) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(274,942) x common factors =2 x 1 = 2
LCM(274,942) = ( 274 × 942 ) / 2
LCM(274,942) = 258108 / 2
LCM(274,942) = 129054
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FAQs on GCF of Fractions of 6419/274, 3430/942
1. What is the HCF of 6419,3430?
The HCF of 6419,3430 is 49
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 6419/274, 3430/942?
Answer: GCF of Numerators as per given numbers 6419/274, 3430/942 is
GCF of Numerators i.e. for 6419,3430 is 49
LCM of denominators i.e. for 274,942 is 129054.
Thus, GCF of Fractions is 49/129054.Finally, GCF of Fractions for 6419/274, 3430/942 is 49/129054.