GCF of 7743/171, 1980/663
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7743/171, 1980/663 i.e 3/37791 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7743/171, 1980/663.
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 7743/171,1980/663?
Given fractions are 7743/171,1980/663
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 7743/171,1980/663, numerators are 7743,1980
Denominators are 171,663
The GCF of 7743,1980 is 3 .
LCM of 171,663 is 37791.
The greatest common factor of 7743/171,1980/663 = [GCF of 7743,1980]/[LCM of 171,663]= 3/37791
Therefore, the GCF of 7743/171,1980/663 is 3/37791.
To find the highest common factor of 7743,1980, we have to find the factors of both numbers and list the highest common factor.
The factors of 7743 are 1, 3, 29, 87, 89, 267, 2581, 7743
The factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980
The HCF of 7743,1980 is 3.
Lets's calculate GCF of 7743,1980
| 3 | 7743, 1980 |
| 2581, 660 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7743,1980 By Matching Biggest Common Factor Method
Now, list down the factors of 7743
:1,3,29,87,89,267,2581,7743
Now, list down the factors of 1980
:1,2,3,4,5,6,9,10,11,12,15,18,20,22,30,33,36,44,45,55,60,66,90,99,110,132,165,180,198,220,330,396,495,660,990,1980
Greatest Common Factor
We found the factors 7743,1980 . The biggest common factor number is the GCF number.
So the greatest common factor 7743,1980 is 3.
Lets's calculate LCM of 171,663
| 3 | 171, 663 |
| 57, 221 |
∴ So the LCM of the given numbers is 3 x 57 x 221 = 37791
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/37791
Therefore, the GCF of Fractions 7743/171,1980/663 is 3/37791
Least Common Multiple of 171,663 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 171,663 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(171,663) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(171,663) x common factors =3 x 1 = 3
LCM(171,663) = ( 171 × 663 ) / 3
LCM(171,663) = 113373 / 3
LCM(171,663) = 37791
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FAQs on GCF of Fractions of 7743/171, 1980/663
1. What is the HCF of 7743,1980?
The HCF of 7743,1980 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 7743/171, 1980/663?
Answer: GCF of Numerators as per given numbers 7743/171, 1980/663 is
GCF of Numerators i.e. for 7743,1980 is 3
LCM of denominators i.e. for 171,663 is 37791.
Thus, GCF of Fractions is 3/37791.Finally, GCF of Fractions for 7743/171, 1980/663 is 3/37791.