GCF of 981/205, 5742/415
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 981/205, 5742/415 i.e 9/17015 easily. The following is the detailed procedure to determine the greatest common factor of fractions 981/205, 5742/415.
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 981/205,5742/415?
Given fractions are 981/205,5742/415
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 981/205,5742/415, numerators are 981,5742
Denominators are 205,415
The GCF of 981,5742 is 9 .
LCM of 205,415 is 17015.
The greatest common factor of 981/205,5742/415 = [GCF of 981,5742]/[LCM of 205,415]= 9/17015
Therefore, the GCF of 981/205,5742/415 is 9/17015.
To find the highest common factor of 981,5742, we have to find the factors of both numbers and list the highest common factor.
The factors of 981 are 1, 3, 9, 109, 327, 981
The factors of 5742 are 1, 2, 3, 6, 9, 11, 18, 22, 29, 33, 58, 66, 87, 99, 174, 198, 261, 319, 522, 638, 957, 1914, 2871, 5742
The HCF of 981,5742 is 9.
Lets's calculate GCF of 981,5742
| 3 | 981, 5742 |
| 3 | 327, 1914 |
| 109, 638 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 981,5742 By Matching Biggest Common Factor Method
Now, list down the factors of 981
:1,3,9,109,327,981
Now, list down the factors of 5742
:1,2,3,6,9,11,18,22,29,33,58,66,87,99,174,198,261,319,522,638,957,1914,2871,5742
Greatest Common Factor
We found the factors 981,5742 . The biggest common factor number is the GCF number.
So the greatest common factor 981,5742 is 9.
Lets's calculate LCM of 205,415
| 5 | 205, 415 |
| 41, 83 |
∴ So the LCM of the given numbers is 5 x 41 x 83 = 17015
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/17015
Therefore, the GCF of Fractions 981/205,5742/415 is 9/17015
Least Common Multiple of 205,415 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 205,415 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,415) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(205,415) x common factors =5 x 1 = 5
LCM(205,415) = ( 205 × 415 ) / 5
LCM(205,415) = 85075 / 5
LCM(205,415) = 17015
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FAQs on GCF of Fractions of 981/205, 5742/415
1. What is the HCF of 981,5742?
The HCF of 981,5742 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 981/205, 5742/415?
Answer: GCF of Numerators as per given numbers 981/205, 5742/415 is
GCF of Numerators i.e. for 981,5742 is 9
LCM of denominators i.e. for 205,415 is 17015.
Thus, GCF of Fractions is 9/17015.Finally, GCF of Fractions for 981/205, 5742/415 is 9/17015.