GCF of 384/185, 6174/2177
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 384/185, 6174/2177 i.e 6/402745 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/185, 6174/2177.
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 384/185,6174/2177?
Given fractions are 384/185,6174/2177
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 384/185,6174/2177, numerators are 384,6174
Denominators are 185,2177
The GCF of 384,6174 is 6 .
LCM of 185,2177 is 402745.
The greatest common factor of 384/185,6174/2177 = [GCF of 384,6174]/[LCM of 185,2177]= 6/402745
Therefore, the GCF of 384/185,6174/2177 is 6/402745.
To find the highest common factor of 384,6174, 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 6174 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441, 686, 882, 1029, 2058, 3087, 6174
The HCF of 384,6174 is 6.
Lets's calculate GCF of 384,6174
| 2 | 384, 6174 |
| 3 | 192, 3087 |
| 64, 1029 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 384,6174 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 6174
:1,2,3,6,7,9,14,18,21,42,49,63,98,126,147,294,343,441,686,882,1029,2058,3087,6174
Greatest Common Factor
We found the factors 384,6174 . The biggest common factor number is the GCF number.
So the greatest common factor 384,6174 is 6.
Lets's calculate LCM of 185,2177
Given numbers has no common factors except 1. So, there LCM is their product i.e 402745
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/402745
Therefore, the GCF of Fractions 384/185,6174/2177 is 6/402745
Least Common Multiple of 185,2177 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 185,2177 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(185,2177) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(185,2177) x common factors =1 x 1 = 1
LCM(185,2177) = ( 185 × 2177 ) / 1
LCM(185,2177) = 402745 / 1
LCM(185,2177) = 402745
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 384/185, 6174/2177
1. What is the HCF of 384,6174?
The HCF of 384,6174 is 6
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 384/185, 6174/2177?
Answer: GCF of Numerators as per given numbers 384/185, 6174/2177 is
GCF of Numerators i.e. for 384,6174 is 6
LCM of denominators i.e. for 185,2177 is 402745.
Thus, GCF of Fractions is 6/402745.Finally, GCF of Fractions for 384/185, 6174/2177 is 6/402745.