GCF of 8109/474, 1998/4661
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8109/474, 1998/4661 i.e 9/27966 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8109/474, 1998/4661.
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 8109/474,1998/4661?
Given fractions are 8109/474,1998/4661
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 8109/474,1998/4661, numerators are 8109,1998
Denominators are 474,4661
The GCF of 8109,1998 is 9 .
LCM of 474,4661 is 27966.
The greatest common factor of 8109/474,1998/4661 = [GCF of 8109,1998]/[LCM of 474,4661]= 9/27966
Therefore, the GCF of 8109/474,1998/4661 is 9/27966.
To find the highest common factor of 8109,1998, we have to find the factors of both numbers and list the highest common factor.
The factors of 8109 are 1, 3, 9, 17, 51, 53, 153, 159, 477, 901, 2703, 8109
The factors of 1998 are 1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 111, 222, 333, 666, 999, 1998
The HCF of 8109,1998 is 9.
Lets's calculate GCF of 8109,1998
| 3 | 8109, 1998 |
| 3 | 2703, 666 |
| 901, 222 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 8109,1998 By Matching Biggest Common Factor Method
Now, list down the factors of 8109
:1,3,9,17,51,53,153,159,477,901,2703,8109
Now, list down the factors of 1998
:1,2,3,6,9,18,27,37,54,74,111,222,333,666,999,1998
Greatest Common Factor
We found the factors 8109,1998 . The biggest common factor number is the GCF number.
So the greatest common factor 8109,1998 is 9.
Lets's calculate LCM of 474,4661
| 79 | 474, 4661 |
| 6, 59 |
∴ So the LCM of the given numbers is 79 x 6 x 59 = 27966
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/27966
Therefore, the GCF of Fractions 8109/474,1998/4661 is 9/27966
Least Common Multiple of 474,4661 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 474,4661 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(474,4661) = 79
common factors(in case of two or more numbers have common factors) = 1
GCF(474,4661) x common factors =79 x 1 = 79
LCM(474,4661) = ( 474 × 4661 ) / 79
LCM(474,4661) = 2209314 / 79
LCM(474,4661) = 27966
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FAQs on GCF of Fractions of 8109/474, 1998/4661
1. What is the HCF of 8109,1998?
The HCF of 8109,1998 is 9
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 8109/474, 1998/4661?
Answer: GCF of Numerators as per given numbers 8109/474, 1998/4661 is
GCF of Numerators i.e. for 8109,1998 is 9
LCM of denominators i.e. for 474,4661 is 27966.
Thus, GCF of Fractions is 9/27966.Finally, GCF of Fractions for 8109/474, 1998/4661 is 9/27966.