GCF of 7786/687, 4760/6809
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7786/687, 4760/6809 i.e 34/4677783 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7786/687, 4760/6809.
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 7786/687,4760/6809?
Given fractions are 7786/687,4760/6809
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 7786/687,4760/6809, numerators are 7786,4760
Denominators are 687,6809
The GCF of 7786,4760 is 34 .
LCM of 687,6809 is 4677783.
The greatest common factor of 7786/687,4760/6809 = [GCF of 7786,4760]/[LCM of 687,6809]= 34/4677783
Therefore, the GCF of 7786/687,4760/6809 is 34/4677783.
To find the highest common factor of 7786,4760, we have to find the factors of both numbers and list the highest common factor.
The factors of 7786 are 1, 2, 17, 34, 229, 458, 3893, 7786
The factors of 4760 are 1, 2, 4, 5, 7, 8, 10, 14, 17, 20, 28, 34, 35, 40, 56, 68, 70, 85, 119, 136, 140, 170, 238, 280, 340, 476, 595, 680, 952, 1190, 2380, 4760
The HCF of 7786,4760 is 34.
Lets's calculate GCF of 7786,4760
| 2 | 7786, 4760 |
| 17 | 3893, 2380 |
| 229, 140 |
∴ So the GCF of the given numbers is 2 x 17 = 34
Greatest Common Factor of 7786,4760 By Matching Biggest Common Factor Method
Now, list down the factors of 7786
:1,2,17,34,229,458,3893,7786
Now, list down the factors of 4760
:1,2,4,5,7,8,10,14,17,20,28,34,35,40,56,68,70,85,119,136,140,170,238,280,340,476,595,680,952,1190,2380,4760
Greatest Common Factor
We found the factors 7786,4760 . The biggest common factor number is the GCF number.
So the greatest common factor 7786,4760 is 34.
Lets's calculate LCM of 687,6809
Given numbers has no common factors except 1. So, there LCM is their product i.e 4677783
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/4677783
Therefore, the GCF of Fractions 7786/687,4760/6809 is 34/4677783
Least Common Multiple of 687,6809 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 687,6809 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(687,6809) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(687,6809) x common factors =1 x 1 = 1
LCM(687,6809) = ( 687 × 6809 ) / 1
LCM(687,6809) = 4677783 / 1
LCM(687,6809) = 4677783
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FAQs on GCF of Fractions of 7786/687, 4760/6809
1. What is the HCF of 7786,4760?
The HCF of 7786,4760 is 34
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 7786/687, 4760/6809?
Answer: GCF of Numerators as per given numbers 7786/687, 4760/6809 is
GCF of Numerators i.e. for 7786,4760 is 34
LCM of denominators i.e. for 687,6809 is 4677783.
Thus, GCF of Fractions is 34/4677783.Finally, GCF of Fractions for 7786/687, 4760/6809 is 34/4677783.