GCF of 819/91, 343/269
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 819/91, 343/269 i.e 7/24479 easily. The following is the detailed procedure to determine the greatest common factor of fractions 819/91, 343/269.
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 819/91,343/269?
Given fractions are 819/91,343/269
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 819/91,343/269, numerators are 819,343
Denominators are 91,269
The GCF of 819,343 is 7 .
LCM of 91,269 is 24479.
The greatest common factor of 819/91,343/269 = [GCF of 819,343]/[LCM of 91,269]= 7/24479
Therefore, the GCF of 819/91,343/269 is 7/24479.
To find the highest common factor of 819,343, we have to find the factors of both numbers and list the highest common factor.
The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
The factors of 343 are 1, 7, 49, 343
The HCF of 819,343 is 7.
Lets's calculate GCF of 819,343
| 7 | 819, 343 |
| 117, 49 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 819,343 By Matching Biggest Common Factor Method
Now, list down the factors of 819
:1,3,7,9,13,21,39,63,91,117,273,819
Now, list down the factors of 343
:1,7,49,343
Greatest Common Factor
We found the factors 819,343 . The biggest common factor number is the GCF number.
So the greatest common factor 819,343 is 7.
Lets's calculate LCM of 91,269
Given numbers has no common factors except 1. So, there LCM is their product i.e 24479
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/24479
Therefore, the GCF of Fractions 819/91,343/269 is 7/24479
Least Common Multiple of 91,269 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 91,269 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(91,269) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(91,269) x common factors =1 x 1 = 1
LCM(91,269) = ( 91 × 269 ) / 1
LCM(91,269) = 24479 / 1
LCM(91,269) = 24479
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FAQs on GCF of Fractions of 819/91, 343/269
1. What is the HCF of 819,343?
The HCF of 819,343 is 7
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 819/91, 343/269?
Answer: GCF of Numerators as per given numbers 819/91, 343/269 is
GCF of Numerators i.e. for 819,343 is 7
LCM of denominators i.e. for 91,269 is 24479.
Thus, GCF of Fractions is 7/24479.Finally, GCF of Fractions for 819/91, 343/269 is 7/24479.