GCF of 6769/286, 8227/1684
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6769/286, 8227/1684 i.e 1/240812 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6769/286, 8227/1684.
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 6769/286,8227/1684?
Given fractions are 6769/286,8227/1684
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 6769/286,8227/1684, numerators are 6769,8227
Denominators are 286,1684
The GCF of 6769,8227 is 1 .
LCM of 286,1684 is 240812.
The greatest common factor of 6769/286,8227/1684 = [GCF of 6769,8227]/[LCM of 286,1684]= 1/240812
Therefore, the GCF of 6769/286,8227/1684 is 1/240812.
To find the highest common factor of 6769,8227, we have to find the factors of both numbers and list the highest common factor.
The factors of 6769 are 1, 7, 967, 6769
The factors of 8227 are 1, 19, 433, 8227
The HCF of 6769,8227 is 1.
Lets's calculate GCF of 6769,8227
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 6769,8227 By Matching Biggest Common Factor Method
Now, list down the factors of 6769
:1,7,967,6769
Now, list down the factors of 8227
:1,19,433,8227
Greatest Common Factor
We found the factors 6769,8227 . The biggest common factor number is the GCF number.
So the greatest common factor 6769,8227 is 1.
Lets's calculate LCM of 286,1684
| 2 | 286, 1684 |
| 143, 842 |
∴ So the LCM of the given numbers is 2 x 143 x 842 = 240812
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/240812
Therefore, the GCF of Fractions 6769/286,8227/1684 is 1/240812
Least Common Multiple of 286,1684 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 286,1684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(286,1684) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(286,1684) x common factors =2 x 1 = 2
LCM(286,1684) = ( 286 × 1684 ) / 2
LCM(286,1684) = 481624 / 2
LCM(286,1684) = 240812
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FAQs on GCF of Fractions of 6769/286, 8227/1684
1. What is the HCF of 6769,8227?
The HCF of 6769,8227 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 6769/286, 8227/1684?
Answer: GCF of Numerators as per given numbers 6769/286, 8227/1684 is
GCF of Numerators i.e. for 6769,8227 is 1
LCM of denominators i.e. for 286,1684 is 240812.
Thus, GCF of Fractions is 1/240812.Finally, GCF of Fractions for 6769/286, 8227/1684 is 1/240812.