GCF of 7668/366, 7830/6797
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7668/366, 7830/6797 i.e 54/2487702 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7668/366, 7830/6797.
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 7668/366,7830/6797?
Given fractions are 7668/366,7830/6797
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 7668/366,7830/6797, numerators are 7668,7830
Denominators are 366,6797
The GCF of 7668,7830 is 54 .
LCM of 366,6797 is 2487702.
The greatest common factor of 7668/366,7830/6797 = [GCF of 7668,7830]/[LCM of 366,6797]= 54/2487702
Therefore, the GCF of 7668/366,7830/6797 is 54/2487702.
To find the highest common factor of 7668,7830, we have to find the factors of both numbers and list the highest common factor.
The factors of 7668 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 71, 108, 142, 213, 284, 426, 639, 852, 1278, 1917, 2556, 3834, 7668
The factors of 7830 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 29, 30, 45, 54, 58, 87, 90, 135, 145, 174, 261, 270, 290, 435, 522, 783, 870, 1305, 1566, 2610, 3915, 7830
The HCF of 7668,7830 is 54.
Lets's calculate GCF of 7668,7830
| 2 | 7668, 7830 |
| 3 | 3834, 3915 |
| 3 | 1278, 1305 |
| 3 | 426, 435 |
| 142, 145 |
∴ So the GCF of the given numbers is 2 x 3 x 3 x 3 = 54
Greatest Common Factor of 7668,7830 By Matching Biggest Common Factor Method
Now, list down the factors of 7668
:1,2,3,4,6,9,12,18,27,36,54,71,108,142,213,284,426,639,852,1278,1917,2556,3834,7668
Now, list down the factors of 7830
:1,2,3,5,6,9,10,15,18,27,29,30,45,54,58,87,90,135,145,174,261,270,290,435,522,783,870,1305,1566,2610,3915,7830
Greatest Common Factor
We found the factors 7668,7830 . The biggest common factor number is the GCF number.
So the greatest common factor 7668,7830 is 54.
Lets's calculate LCM of 366,6797
Given numbers has no common factors except 1. So, there LCM is their product i.e 2487702
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 54/2487702
Therefore, the GCF of Fractions 7668/366,7830/6797 is 54/2487702
Least Common Multiple of 366,6797 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 366,6797 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(366,6797) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(366,6797) x common factors =1 x 1 = 1
LCM(366,6797) = ( 366 × 6797 ) / 1
LCM(366,6797) = 2487702 / 1
LCM(366,6797) = 2487702
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FAQs on GCF of Fractions of 7668/366, 7830/6797
1. What is the HCF of 7668,7830?
The HCF of 7668,7830 is 54
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 7668/366, 7830/6797?
Answer: GCF of Numerators as per given numbers 7668/366, 7830/6797 is
GCF of Numerators i.e. for 7668,7830 is 54
LCM of denominators i.e. for 366,6797 is 2487702.
Thus, GCF of Fractions is 54/2487702.Finally, GCF of Fractions for 7668/366, 7830/6797 is 54/2487702.