GCF of 192/174, 1005/361
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 192/174, 1005/361 i.e 3/62814 easily. The following is the detailed procedure to determine the greatest common factor of fractions 192/174, 1005/361.
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 192/174,1005/361?
Given fractions are 192/174,1005/361
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 192/174,1005/361, numerators are 192,1005
Denominators are 174,361
The GCF of 192,1005 is 3 .
LCM of 174,361 is 62814.
The greatest common factor of 192/174,1005/361 = [GCF of 192,1005]/[LCM of 174,361]= 3/62814
Therefore, the GCF of 192/174,1005/361 is 3/62814.
To find the highest common factor of 192,1005, we have to find the factors of both numbers and list the highest common factor.
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
The factors of 1005 are 1, 3, 5, 15, 67, 201, 335, 1005
The HCF of 192,1005 is 3.
Lets's calculate GCF of 192,1005
| 3 | 192, 1005 |
| 64, 335 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 192,1005 By Matching Biggest Common Factor Method
Now, list down the factors of 192
:1,2,3,4,6,8,12,16,24,32,48,64,96,192
Now, list down the factors of 1005
:1,3,5,15,67,201,335,1005
Greatest Common Factor
We found the factors 192,1005 . The biggest common factor number is the GCF number.
So the greatest common factor 192,1005 is 3.
Lets's calculate LCM of 174,361
Given numbers has no common factors except 1. So, there LCM is their product i.e 62814
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/62814
Therefore, the GCF of Fractions 192/174,1005/361 is 3/62814
Least Common Multiple of 174,361 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 174,361 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(174,361) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(174,361) x common factors =1 x 1 = 1
LCM(174,361) = ( 174 × 361 ) / 1
LCM(174,361) = 62814 / 1
LCM(174,361) = 62814
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FAQs on GCF of Fractions of 192/174, 1005/361
1. What is the HCF of 192,1005?
The HCF of 192,1005 is 3
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 192/174, 1005/361?
Answer: GCF of Numerators as per given numbers 192/174, 1005/361 is
GCF of Numerators i.e. for 192,1005 is 3
LCM of denominators i.e. for 174,361 is 62814.
Thus, GCF of Fractions is 3/62814.Finally, GCF of Fractions for 192/174, 1005/361 is 3/62814.