GCF of 398/405, 6140/5109
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 398/405, 6140/5109 i.e 2/689715 easily. The following is the detailed procedure to determine the greatest common factor of fractions 398/405, 6140/5109.
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 398/405,6140/5109?
Given fractions are 398/405,6140/5109
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 398/405,6140/5109, numerators are 398,6140
Denominators are 405,5109
The GCF of 398,6140 is 2 .
LCM of 405,5109 is 689715.
The greatest common factor of 398/405,6140/5109 = [GCF of 398,6140]/[LCM of 405,5109]= 2/689715
Therefore, the GCF of 398/405,6140/5109 is 2/689715.
To find the highest common factor of 398,6140, we have to find the factors of both numbers and list the highest common factor.
The factors of 398 are 1, 2, 199, 398
The factors of 6140 are 1, 2, 4, 5, 10, 20, 307, 614, 1228, 1535, 3070, 6140
The HCF of 398,6140 is 2.
Lets's calculate GCF of 398,6140
| 2 | 398, 6140 |
| 199, 3070 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 398,6140 By Matching Biggest Common Factor Method
Now, list down the factors of 398
:1,2,199,398
Now, list down the factors of 6140
:1,2,4,5,10,20,307,614,1228,1535,3070,6140
Greatest Common Factor
We found the factors 398,6140 . The biggest common factor number is the GCF number.
So the greatest common factor 398,6140 is 2.
Lets's calculate LCM of 405,5109
| 3 | 405, 5109 |
| 135, 1703 |
∴ So the LCM of the given numbers is 3 x 135 x 1703 = 689715
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/689715
Therefore, the GCF of Fractions 398/405,6140/5109 is 2/689715
Least Common Multiple of 405,5109 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 405,5109 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(405,5109) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(405,5109) x common factors =3 x 1 = 3
LCM(405,5109) = ( 405 × 5109 ) / 3
LCM(405,5109) = 2069145 / 3
LCM(405,5109) = 689715
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FAQs on GCF of Fractions of 398/405, 6140/5109
1. What is the HCF of 398,6140?
The HCF of 398,6140 is 2
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 398/405, 6140/5109?
Answer: GCF of Numerators as per given numbers 398/405, 6140/5109 is
GCF of Numerators i.e. for 398,6140 is 2
LCM of denominators i.e. for 405,5109 is 689715.
Thus, GCF of Fractions is 2/689715.Finally, GCF of Fractions for 398/405, 6140/5109 is 2/689715.