GCF of 7686/468, 3649/786
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7686/468, 3649/786 i.e 1/61308 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7686/468, 3649/786.
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 7686/468,3649/786?
Given fractions are 7686/468,3649/786
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 7686/468,3649/786, numerators are 7686,3649
Denominators are 468,786
The GCF of 7686,3649 is 1 .
LCM of 468,786 is 61308.
The greatest common factor of 7686/468,3649/786 = [GCF of 7686,3649]/[LCM of 468,786]= 1/61308
Therefore, the GCF of 7686/468,3649/786 is 1/61308.
To find the highest common factor of 7686,3649, we have to find the factors of both numbers and list the highest common factor.
The factors of 7686 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 61, 63, 122, 126, 183, 366, 427, 549, 854, 1098, 1281, 2562, 3843, 7686
The factors of 3649 are 1, 41, 89, 3649
The HCF of 7686,3649 is 1.
Lets's calculate GCF of 7686,3649
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7686,3649 By Matching Biggest Common Factor Method
Now, list down the factors of 7686
:1,2,3,6,7,9,14,18,21,42,61,63,122,126,183,366,427,549,854,1098,1281,2562,3843,7686
Now, list down the factors of 3649
:1,41,89,3649
Greatest Common Factor
We found the factors 7686,3649 . The biggest common factor number is the GCF number.
So the greatest common factor 7686,3649 is 1.
Lets's calculate LCM of 468,786
| 2 | 468, 786 |
| 3 | 234, 393 |
| 78, 131 |
∴ So the LCM of the given numbers is 2 x 3 x 78 x 131 = 61308
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/61308
Therefore, the GCF of Fractions 7686/468,3649/786 is 1/61308
Least Common Multiple of 468,786 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 468,786 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(468,786) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(468,786) x common factors =6 x 1 = 6
LCM(468,786) = ( 468 × 786 ) / 6
LCM(468,786) = 367848 / 6
LCM(468,786) = 61308
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 7686/468, 3649/786
1. What is the HCF of 7686,3649?
The HCF of 7686,3649 is 1
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 7686/468, 3649/786?
Answer: GCF of Numerators as per given numbers 7686/468, 3649/786 is
GCF of Numerators i.e. for 7686,3649 is 1
LCM of denominators i.e. for 468,786 is 61308.
Thus, GCF of Fractions is 1/61308.Finally, GCF of Fractions for 7686/468, 3649/786 is 1/61308.