GCF of 4270/378, 9890/8192
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4270/378, 9890/8192 i.e 10/1548288 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4270/378, 9890/8192.
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 4270/378,9890/8192?
Given fractions are 4270/378,9890/8192
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 4270/378,9890/8192, numerators are 4270,9890
Denominators are 378,8192
The GCF of 4270,9890 is 10 .
LCM of 378,8192 is 1548288.
The greatest common factor of 4270/378,9890/8192 = [GCF of 4270,9890]/[LCM of 378,8192]= 10/1548288
Therefore, the GCF of 4270/378,9890/8192 is 10/1548288.
To find the highest common factor of 4270,9890, we have to find the factors of both numbers and list the highest common factor.
The factors of 4270 are 1, 2, 5, 7, 10, 14, 35, 61, 70, 122, 305, 427, 610, 854, 2135, 4270
The factors of 9890 are 1, 2, 5, 10, 23, 43, 46, 86, 115, 215, 230, 430, 989, 1978, 4945, 9890
The HCF of 4270,9890 is 10.
Lets's calculate GCF of 4270,9890
| 2 | 4270, 9890 |
| 5 | 2135, 4945 |
| 427, 989 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 4270,9890 By Matching Biggest Common Factor Method
Now, list down the factors of 4270
:1,2,5,7,10,14,35,61,70,122,305,427,610,854,2135,4270
Now, list down the factors of 9890
:1,2,5,10,23,43,46,86,115,215,230,430,989,1978,4945,9890
Greatest Common Factor
We found the factors 4270,9890 . The biggest common factor number is the GCF number.
So the greatest common factor 4270,9890 is 10.
Lets's calculate LCM of 378,8192
| 2 | 378, 8192 |
| 189, 4096 |
∴ So the LCM of the given numbers is 2 x 189 x 4096 = 1548288
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/1548288
Therefore, the GCF of Fractions 4270/378,9890/8192 is 10/1548288
Least Common Multiple of 378,8192 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 378,8192 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(378,8192) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(378,8192) x common factors =2 x 1 = 2
LCM(378,8192) = ( 378 × 8192 ) / 2
LCM(378,8192) = 3096576 / 2
LCM(378,8192) = 1548288
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 4270/378, 9890/8192
1. What is the HCF of 4270,9890?
The HCF of 4270,9890 is 10
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 4270/378, 9890/8192?
Answer: GCF of Numerators as per given numbers 4270/378, 9890/8192 is
GCF of Numerators i.e. for 4270,9890 is 10
LCM of denominators i.e. for 378,8192 is 1548288.
Thus, GCF of Fractions is 10/1548288.Finally, GCF of Fractions for 4270/378, 9890/8192 is 10/1548288.