GCF of 206/96, 112/192
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 206/96, 112/192 i.e 2/192 easily. The following is the detailed procedure to determine the greatest common factor of fractions 206/96, 112/192.
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 206/96,112/192?
Given fractions are 206/96,112/192
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 206/96,112/192, numerators are 206,112
Denominators are 96,192
The GCF of 206,112 is 2 .
LCM of 96,192 is 192.
The greatest common factor of 206/96,112/192 = [GCF of 206,112]/[LCM of 96,192]= 2/192
Therefore, the GCF of 206/96,112/192 is 2/192.
To find the highest common factor of 206,112, we have to find the factors of both numbers and list the highest common factor.
The factors of 206 are 1, 2, 103, 206
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
The HCF of 206,112 is 2.
Lets's calculate GCF of 206,112
| 2 | 206, 112 |
| 103, 56 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 206,112 By Matching Biggest Common Factor Method
Now, list down the factors of 206
:1,2,103,206
Now, list down the factors of 112
:1,2,4,7,8,14,16,28,56,112
Greatest Common Factor
We found the factors 206,112 . The biggest common factor number is the GCF number.
So the greatest common factor 206,112 is 2.
Lets's calculate LCM of 96,192
| 2 | 96, 192 |
| 2 | 48, 96 |
| 2 | 24, 48 |
| 2 | 12, 24 |
| 2 | 6, 12 |
| 3 | 3, 6 |
| 1, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 1 x 2 = 192
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/192
Therefore, the GCF of Fractions 206/96,112/192 is 2/192
Least Common Multiple of 96,192 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 96,192 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,192) = 96
common factors(in case of two or more numbers have common factors) = 1
GCF(96,192) x common factors =96 x 1 = 96
LCM(96,192) = ( 96 × 192 ) / 96
LCM(96,192) = 18432 / 96
LCM(96,192) = 192
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FAQs on GCF of Fractions of 206/96, 112/192
1. What is the HCF of 206,112?
The HCF of 206,112 is 2
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 206/96, 112/192?
Answer: GCF of Numerators as per given numbers 206/96, 112/192 is
GCF of Numerators i.e. for 206,112 is 2
LCM of denominators i.e. for 96,192 is 192.
Thus, GCF of Fractions is 2/192.Finally, GCF of Fractions for 206/96, 112/192 is 2/192.