GCF of 2500/407, 6540/9713
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2500/407, 6540/9713 i.e 20/359381 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2500/407, 6540/9713.
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 2500/407,6540/9713?
Given fractions are 2500/407,6540/9713
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 2500/407,6540/9713, numerators are 2500,6540
Denominators are 407,9713
The GCF of 2500,6540 is 20 .
LCM of 407,9713 is 359381.
The greatest common factor of 2500/407,6540/9713 = [GCF of 2500,6540]/[LCM of 407,9713]= 20/359381
Therefore, the GCF of 2500/407,6540/9713 is 20/359381.
To find the highest common factor of 2500,6540, we have to find the factors of both numbers and list the highest common factor.
The factors of 2500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500
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 HCF of 2500,6540 is 20.
Lets's calculate GCF of 2500,6540
| 2 | 2500, 6540 |
| 2 | 1250, 3270 |
| 5 | 625, 1635 |
| 125, 327 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 2500,6540 By Matching Biggest Common Factor Method
Now, list down the factors of 2500
:1,2,4,5,10,20,25,50,100,125,250,500,625,1250,2500
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
Greatest Common Factor
We found the factors 2500,6540 . The biggest common factor number is the GCF number.
So the greatest common factor 2500,6540 is 20.
Lets's calculate LCM of 407,9713
| 11 | 407, 9713 |
| 37, 883 |
∴ So the LCM of the given numbers is 11 x 37 x 883 = 359381
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/359381
Therefore, the GCF of Fractions 2500/407,6540/9713 is 20/359381
Least Common Multiple of 407,9713 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 407,9713 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(407,9713) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(407,9713) x common factors =11 x 1 = 11
LCM(407,9713) = ( 407 × 9713 ) / 11
LCM(407,9713) = 3953191 / 11
LCM(407,9713) = 359381
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FAQs on GCF of Fractions of 2500/407, 6540/9713
1. What is the HCF of 2500,6540?
The HCF of 2500,6540 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 2500/407, 6540/9713?
Answer: GCF of Numerators as per given numbers 2500/407, 6540/9713 is
GCF of Numerators i.e. for 2500,6540 is 20
LCM of denominators i.e. for 407,9713 is 359381.
Thus, GCF of Fractions is 20/359381.Finally, GCF of Fractions for 2500/407, 6540/9713 is 20/359381.