GCF of 133/328, 7182/192
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 133/328, 7182/192 i.e 133/7872 easily. The following is the detailed procedure to determine the greatest common factor of fractions 133/328, 7182/192.
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 133/328,7182/192?
Given fractions are 133/328,7182/192
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 133/328,7182/192, numerators are 133,7182
Denominators are 328,192
The GCF of 133,7182 is 133 .
LCM of 328,192 is 7872.
The greatest common factor of 133/328,7182/192 = [GCF of 133,7182]/[LCM of 328,192]= 133/7872
Therefore, the GCF of 133/328,7182/192 is 133/7872.
To find the highest common factor of 133,7182, we have to find the factors of both numbers and list the highest common factor.
The factors of 133 are 1, 7, 19, 133
The factors of 7182 are 1, 2, 3, 6, 7, 9, 14, 18, 19, 21, 27, 38, 42, 54, 57, 63, 114, 126, 133, 171, 189, 266, 342, 378, 399, 513, 798, 1026, 1197, 2394, 3591, 7182
The HCF of 133,7182 is 133.
Lets's calculate GCF of 133,7182
| 7 | 133, 7182 |
| 19 | 19, 1026 |
| 1, 54 |
∴ So the GCF of the given numbers is 7 x 19 = 133
Greatest Common Factor of 133,7182 By Matching Biggest Common Factor Method
Now, list down the factors of 133
:1,7,19,133
Now, list down the factors of 7182
:1,2,3,6,7,9,14,18,19,21,27,38,42,54,57,63,114,126,133,171,189,266,342,378,399,513,798,1026,1197,2394,3591,7182
Greatest Common Factor
We found the factors 133,7182 . The biggest common factor number is the GCF number.
So the greatest common factor 133,7182 is 133.
Lets's calculate LCM of 328,192
| 2 | 328, 192 |
| 2 | 164, 96 |
| 2 | 82, 48 |
| 41, 24 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 41 x 24 = 7872
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 133/7872
Therefore, the GCF of Fractions 133/328,7182/192 is 133/7872
Least Common Multiple of 328,192 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 328,192 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(328,192) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(328,192) x common factors =8 x 1 = 8
LCM(328,192) = ( 328 × 192 ) / 8
LCM(328,192) = 62976 / 8
LCM(328,192) = 7872
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FAQs on GCF of Fractions of 133/328, 7182/192
1. What is the HCF of 133,7182?
The HCF of 133,7182 is 133
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 133/328, 7182/192?
Answer: GCF of Numerators as per given numbers 133/328, 7182/192 is
GCF of Numerators i.e. for 133,7182 is 133
LCM of denominators i.e. for 328,192 is 7872.
Thus, GCF of Fractions is 133/7872.Finally, GCF of Fractions for 133/328, 7182/192 is 133/7872.