GCF of 984/21, 108/2099
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 984/21, 108/2099 i.e 12/44079 easily. The following is the detailed procedure to determine the greatest common factor of fractions 984/21, 108/2099.
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 984/21,108/2099?
Given fractions are 984/21,108/2099
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 984/21,108/2099, numerators are 984,108
Denominators are 21,2099
The GCF of 984,108 is 12 .
LCM of 21,2099 is 44079.
The greatest common factor of 984/21,108/2099 = [GCF of 984,108]/[LCM of 21,2099]= 12/44079
Therefore, the GCF of 984/21,108/2099 is 12/44079.
To find the highest common factor of 984,108, we have to find the factors of both numbers and list the highest common factor.
The factors of 984 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The HCF of 984,108 is 12.
Lets's calculate GCF of 984,108
| 2 | 984, 108 |
| 2 | 492, 54 |
| 3 | 246, 27 |
| 82, 9 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 984,108 By Matching Biggest Common Factor Method
Now, list down the factors of 984
:1,2,3,4,6,8,12,24,41,82,123,164,246,328,492,984
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Greatest Common Factor
We found the factors 984,108 . The biggest common factor number is the GCF number.
So the greatest common factor 984,108 is 12.
Lets's calculate LCM of 21,2099
Given numbers has no common factors except 1. So, there LCM is their product i.e 44079
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/44079
Therefore, the GCF of Fractions 984/21,108/2099 is 12/44079
Least Common Multiple of 21,2099 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 21,2099 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,2099) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(21,2099) x common factors =1 x 1 = 1
LCM(21,2099) = ( 21 × 2099 ) / 1
LCM(21,2099) = 44079 / 1
LCM(21,2099) = 44079
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FAQs on GCF of Fractions of 984/21, 108/2099
1. What is the HCF of 984,108?
The HCF of 984,108 is 12
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 984/21, 108/2099?
Answer: GCF of Numerators as per given numbers 984/21, 108/2099 is
GCF of Numerators i.e. for 984,108 is 12
LCM of denominators i.e. for 21,2099 is 44079.
Thus, GCF of Fractions is 12/44079.Finally, GCF of Fractions for 984/21, 108/2099 is 12/44079.