GCF of 384/77, 469/3971
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 384/77, 469/3971 i.e 1/27797 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/77, 469/3971.
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 384/77,469/3971?
Given fractions are 384/77,469/3971
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 384/77,469/3971, numerators are 384,469
Denominators are 77,3971
The GCF of 384,469 is 1 .
LCM of 77,3971 is 27797.
The greatest common factor of 384/77,469/3971 = [GCF of 384,469]/[LCM of 77,3971]= 1/27797
Therefore, the GCF of 384/77,469/3971 is 1/27797.
To find the highest common factor of 384,469, we have to find the factors of both numbers and list the highest common factor.
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The factors of 469 are 1, 7, 67, 469
The HCF of 384,469 is 1.
Lets's calculate GCF of 384,469
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 384,469 By Matching Biggest Common Factor Method
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Now, list down the factors of 469
:1,7,67,469
Greatest Common Factor
We found the factors 384,469 . The biggest common factor number is the GCF number.
So the greatest common factor 384,469 is 1.
Lets's calculate LCM of 77,3971
| 11 | 77, 3971 |
| 7, 361 |
∴ So the LCM of the given numbers is 11 x 7 x 361 = 27797
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/27797
Therefore, the GCF of Fractions 384/77,469/3971 is 1/27797
Least Common Multiple of 77,3971 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 77,3971 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,3971) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(77,3971) x common factors =11 x 1 = 11
LCM(77,3971) = ( 77 × 3971 ) / 11
LCM(77,3971) = 305767 / 11
LCM(77,3971) = 27797
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FAQs on GCF of Fractions of 384/77, 469/3971
1. What is the HCF of 384,469?
The HCF of 384,469 is 1
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 384/77, 469/3971?
Answer: GCF of Numerators as per given numbers 384/77, 469/3971 is
GCF of Numerators i.e. for 384,469 is 1
LCM of denominators i.e. for 77,3971 is 27797.
Thus, GCF of Fractions is 1/27797.Finally, GCF of Fractions for 384/77, 469/3971 is 1/27797.