GCF of 686/314, 343/877
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 686/314, 343/877 i.e 343/275378 easily. The following is the detailed procedure to determine the greatest common factor of fractions 686/314, 343/877.
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 686/314,343/877?
Given fractions are 686/314,343/877
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 686/314,343/877, numerators are 686,343
Denominators are 314,877
The GCF of 686,343 is 343 .
LCM of 314,877 is 275378.
The greatest common factor of 686/314,343/877 = [GCF of 686,343]/[LCM of 314,877]= 343/275378
Therefore, the GCF of 686/314,343/877 is 343/275378.
To find the highest common factor of 686,343, we have to find the factors of both numbers and list the highest common factor.
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686
The factors of 343 are 1, 7, 49, 343
The HCF of 686,343 is 343.
Lets's calculate GCF of 686,343
| 7 | 686, 343 |
| 7 | 98, 49 |
| 7 | 14, 7 |
| 2, 1 |
∴ So the GCF of the given numbers is 7 x 7 x 7 = 343
Greatest Common Factor of 686,343 By Matching Biggest Common Factor Method
Now, list down the factors of 686
:1,2,7,14,49,98,343,686
Now, list down the factors of 343
:1,7,49,343
Greatest Common Factor
We found the factors 686,343 . The biggest common factor number is the GCF number.
So the greatest common factor 686,343 is 343.
Lets's calculate LCM of 314,877
Given numbers has no common factors except 1. So, there LCM is their product i.e 275378
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 343/275378
Therefore, the GCF of Fractions 686/314,343/877 is 343/275378
Least Common Multiple of 314,877 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 314,877 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(314,877) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(314,877) x common factors =1 x 1 = 1
LCM(314,877) = ( 314 × 877 ) / 1
LCM(314,877) = 275378 / 1
LCM(314,877) = 275378
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FAQs on GCF of Fractions of 686/314, 343/877
1. What is the HCF of 686,343?
The HCF of 686,343 is 343
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 686/314, 343/877?
Answer: GCF of Numerators as per given numbers 686/314, 343/877 is
GCF of Numerators i.e. for 686,343 is 343
LCM of denominators i.e. for 314,877 is 275378.
Thus, GCF of Fractions is 343/275378.Finally, GCF of Fractions for 686/314, 343/877 is 343/275378.