GCF of 7704/274, 9711/7772
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7704/274, 9711/7772 i.e 9/1064764 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7704/274, 9711/7772.
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 7704/274,9711/7772?
Given fractions are 7704/274,9711/7772
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 7704/274,9711/7772, numerators are 7704,9711
Denominators are 274,7772
The GCF of 7704,9711 is 9 .
LCM of 274,7772 is 1064764.
The greatest common factor of 7704/274,9711/7772 = [GCF of 7704,9711]/[LCM of 274,7772]= 9/1064764
Therefore, the GCF of 7704/274,9711/7772 is 9/1064764.
To find the highest common factor of 7704,9711, we have to find the factors of both numbers and list the highest common factor.
The factors of 7704 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 107, 214, 321, 428, 642, 856, 963, 1284, 1926, 2568, 3852, 7704
The factors of 9711 are 1, 3, 9, 13, 39, 83, 117, 249, 747, 1079, 3237, 9711
The HCF of 7704,9711 is 9.
Lets's calculate GCF of 7704,9711
| 3 | 7704, 9711 |
| 3 | 2568, 3237 |
| 856, 1079 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 7704,9711 By Matching Biggest Common Factor Method
Now, list down the factors of 7704
:1,2,3,4,6,8,9,12,18,24,36,72,107,214,321,428,642,856,963,1284,1926,2568,3852,7704
Now, list down the factors of 9711
:1,3,9,13,39,83,117,249,747,1079,3237,9711
Greatest Common Factor
We found the factors 7704,9711 . The biggest common factor number is the GCF number.
So the greatest common factor 7704,9711 is 9.
Lets's calculate LCM of 274,7772
| 2 | 274, 7772 |
| 137, 3886 |
∴ So the LCM of the given numbers is 2 x 137 x 3886 = 1064764
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/1064764
Therefore, the GCF of Fractions 7704/274,9711/7772 is 9/1064764
Least Common Multiple of 274,7772 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 274,7772 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(274,7772) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(274,7772) x common factors =2 x 1 = 2
LCM(274,7772) = ( 274 × 7772 ) / 2
LCM(274,7772) = 2129528 / 2
LCM(274,7772) = 1064764
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 7704/274, 9711/7772
1. What is the HCF of 7704,9711?
The HCF of 7704,9711 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 7704/274, 9711/7772?
Answer: GCF of Numerators as per given numbers 7704/274, 9711/7772 is
GCF of Numerators i.e. for 7704,9711 is 9
LCM of denominators i.e. for 274,7772 is 1064764.
Thus, GCF of Fractions is 9/1064764.Finally, GCF of Fractions for 7704/274, 9711/7772 is 9/1064764.