GCF of 9459/314, 1005/198
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9459/314, 1005/198 i.e 3/31086 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9459/314, 1005/198.
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 9459/314,1005/198?
Given fractions are 9459/314,1005/198
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 9459/314,1005/198, numerators are 9459,1005
Denominators are 314,198
The GCF of 9459,1005 is 3 .
LCM of 314,198 is 31086.
The greatest common factor of 9459/314,1005/198 = [GCF of 9459,1005]/[LCM of 314,198]= 3/31086
Therefore, the GCF of 9459/314,1005/198 is 3/31086.
To find the highest common factor of 9459,1005, we have to find the factors of both numbers and list the highest common factor.
The factors of 9459 are 1, 3, 9, 1051, 3153, 9459
The factors of 1005 are 1, 3, 5, 15, 67, 201, 335, 1005
The HCF of 9459,1005 is 3.
Lets's calculate GCF of 9459,1005
| 3 | 9459, 1005 |
| 3153, 335 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 9459,1005 By Matching Biggest Common Factor Method
Now, list down the factors of 9459
:1,3,9,1051,3153,9459
Now, list down the factors of 1005
:1,3,5,15,67,201,335,1005
Greatest Common Factor
We found the factors 9459,1005 . The biggest common factor number is the GCF number.
So the greatest common factor 9459,1005 is 3.
Lets's calculate LCM of 314,198
| 2 | 314, 198 |
| 157, 99 |
∴ So the LCM of the given numbers is 2 x 157 x 99 = 31086
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/31086
Therefore, the GCF of Fractions 9459/314,1005/198 is 3/31086
Least Common Multiple of 314,198 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 314,198 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(314,198) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(314,198) x common factors =2 x 1 = 2
LCM(314,198) = ( 314 × 198 ) / 2
LCM(314,198) = 62172 / 2
LCM(314,198) = 31086
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FAQs on GCF of Fractions of 9459/314, 1005/198
1. What is the HCF of 9459,1005?
The HCF of 9459,1005 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 9459/314, 1005/198?
Answer: GCF of Numerators as per given numbers 9459/314, 1005/198 is
GCF of Numerators i.e. for 9459,1005 is 3
LCM of denominators i.e. for 314,198 is 31086.
Thus, GCF of Fractions is 3/31086.Finally, GCF of Fractions for 9459/314, 1005/198 is 3/31086.