GCF of 387/305, 2709/3259
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 387/305, 2709/3259 i.e 387/993995 easily. The following is the detailed procedure to determine the greatest common factor of fractions 387/305, 2709/3259.
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 387/305,2709/3259?
Given fractions are 387/305,2709/3259
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 387/305,2709/3259, numerators are 387,2709
Denominators are 305,3259
The GCF of 387,2709 is 387 .
LCM of 305,3259 is 993995.
The greatest common factor of 387/305,2709/3259 = [GCF of 387,2709]/[LCM of 305,3259]= 387/993995
Therefore, the GCF of 387/305,2709/3259 is 387/993995.
To find the highest common factor of 387,2709, we have to find the factors of both numbers and list the highest common factor.
The factors of 387 are 1, 3, 9, 43, 129, 387
The factors of 2709 are 1, 3, 7, 9, 21, 43, 63, 129, 301, 387, 903, 2709
The HCF of 387,2709 is 387.
Lets's calculate GCF of 387,2709
| 3 | 387, 2709 |
| 3 | 129, 903 |
| 43 | 43, 301 |
| 1, 7 |
∴ So the GCF of the given numbers is 3 x 3 x 43 = 387
Greatest Common Factor of 387,2709 By Matching Biggest Common Factor Method
Now, list down the factors of 387
:1,3,9,43,129,387
Now, list down the factors of 2709
:1,3,7,9,21,43,63,129,301,387,903,2709
Greatest Common Factor
We found the factors 387,2709 . The biggest common factor number is the GCF number.
So the greatest common factor 387,2709 is 387.
Lets's calculate LCM of 305,3259
Given numbers has no common factors except 1. So, there LCM is their product i.e 993995
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 387/993995
Therefore, the GCF of Fractions 387/305,2709/3259 is 387/993995
Least Common Multiple of 305,3259 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 305,3259 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(305,3259) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(305,3259) x common factors =1 x 1 = 1
LCM(305,3259) = ( 305 × 3259 ) / 1
LCM(305,3259) = 993995 / 1
LCM(305,3259) = 993995
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FAQs on GCF of Fractions of 387/305, 2709/3259
1. What is the HCF of 387,2709?
The HCF of 387,2709 is 387
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 387/305, 2709/3259?
Answer: GCF of Numerators as per given numbers 387/305, 2709/3259 is
GCF of Numerators i.e. for 387,2709 is 387
LCM of denominators i.e. for 305,3259 is 993995.
Thus, GCF of Fractions is 387/993995.Finally, GCF of Fractions for 387/305, 2709/3259 is 387/993995.