GCF of 4565/472, 1678/686
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4565/472, 1678/686 i.e 1/161896 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4565/472, 1678/686.
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 4565/472,1678/686?
Given fractions are 4565/472,1678/686
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 4565/472,1678/686, numerators are 4565,1678
Denominators are 472,686
The GCF of 4565,1678 is 1 .
LCM of 472,686 is 161896.
The greatest common factor of 4565/472,1678/686 = [GCF of 4565,1678]/[LCM of 472,686]= 1/161896
Therefore, the GCF of 4565/472,1678/686 is 1/161896.
To find the highest common factor of 4565,1678, we have to find the factors of both numbers and list the highest common factor.
The factors of 4565 are 1, 5, 11, 55, 83, 415, 913, 4565
The factors of 1678 are 1, 2, 839, 1678
The HCF of 4565,1678 is 1.
Lets's calculate GCF of 4565,1678
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 4565,1678 By Matching Biggest Common Factor Method
Now, list down the factors of 4565
:1,5,11,55,83,415,913,4565
Now, list down the factors of 1678
:1,2,839,1678
Greatest Common Factor
We found the factors 4565,1678 . The biggest common factor number is the GCF number.
So the greatest common factor 4565,1678 is 1.
Lets's calculate LCM of 472,686
| 2 | 472, 686 |
| 236, 343 |
∴ So the LCM of the given numbers is 2 x 236 x 343 = 161896
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/161896
Therefore, the GCF of Fractions 4565/472,1678/686 is 1/161896
Least Common Multiple of 472,686 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 472,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(472,686) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(472,686) x common factors =2 x 1 = 2
LCM(472,686) = ( 472 × 686 ) / 2
LCM(472,686) = 323792 / 2
LCM(472,686) = 161896
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FAQs on GCF of Fractions of 4565/472, 1678/686
1. What is the HCF of 4565,1678?
The HCF of 4565,1678 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 4565/472, 1678/686?
Answer: GCF of Numerators as per given numbers 4565/472, 1678/686 is
GCF of Numerators i.e. for 4565,1678 is 1
LCM of denominators i.e. for 472,686 is 161896.
Thus, GCF of Fractions is 1/161896.Finally, GCF of Fractions for 4565/472, 1678/686 is 1/161896.