GCF of 6540/407, 3800/509
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6540/407, 3800/509 i.e 20/207163 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6540/407, 3800/509.
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 6540/407,3800/509?
Given fractions are 6540/407,3800/509
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 6540/407,3800/509, numerators are 6540,3800
Denominators are 407,509
The GCF of 6540,3800 is 20 .
LCM of 407,509 is 207163.
The greatest common factor of 6540/407,3800/509 = [GCF of 6540,3800]/[LCM of 407,509]= 20/207163
Therefore, the GCF of 6540/407,3800/509 is 20/207163.
To find the highest common factor of 6540,3800, we have to find the factors of both numbers and list the highest common factor.
The factors of 6540 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 109, 218, 327, 436, 545, 654, 1090, 1308, 1635, 2180, 3270, 6540
The factors of 3800 are 1, 2, 4, 5, 8, 10, 19, 20, 25, 38, 40, 50, 76, 95, 100, 152, 190, 200, 380, 475, 760, 950, 1900, 3800
The HCF of 6540,3800 is 20.
Lets's calculate GCF of 6540,3800
| 2 | 6540, 3800 |
| 2 | 3270, 1900 |
| 5 | 1635, 950 |
| 327, 190 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 6540,3800 By Matching Biggest Common Factor Method
Now, list down the factors of 6540
:1,2,3,4,5,6,10,12,15,20,30,60,109,218,327,436,545,654,1090,1308,1635,2180,3270,6540
Now, list down the factors of 3800
:1,2,4,5,8,10,19,20,25,38,40,50,76,95,100,152,190,200,380,475,760,950,1900,3800
Greatest Common Factor
We found the factors 6540,3800 . The biggest common factor number is the GCF number.
So the greatest common factor 6540,3800 is 20.
Lets's calculate LCM of 407,509
Given numbers has no common factors except 1. So, there LCM is their product i.e 207163
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/207163
Therefore, the GCF of Fractions 6540/407,3800/509 is 20/207163
Least Common Multiple of 407,509 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 407,509 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(407,509) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(407,509) x common factors =1 x 1 = 1
LCM(407,509) = ( 407 × 509 ) / 1
LCM(407,509) = 207163 / 1
LCM(407,509) = 207163
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FAQs on GCF of Fractions of 6540/407, 3800/509
1. What is the HCF of 6540,3800?
The HCF of 6540,3800 is 20
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 6540/407, 3800/509?
Answer: GCF of Numerators as per given numbers 6540/407, 3800/509 is
GCF of Numerators i.e. for 6540,3800 is 20
LCM of denominators i.e. for 407,509 is 207163.
Thus, GCF of Fractions is 20/207163.Finally, GCF of Fractions for 6540/407, 3800/509 is 20/207163.