GCF of 311/576, 678/906
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 311/576, 678/906 i.e 1/86976 easily. The following is the detailed procedure to determine the greatest common factor of fractions 311/576, 678/906.
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 311/576,678/906?
Given fractions are 311/576,678/906
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 311/576,678/906, numerators are 311,678
Denominators are 576,906
The GCF of 311,678 is 1 .
LCM of 576,906 is 86976.
The greatest common factor of 311/576,678/906 = [GCF of 311,678]/[LCM of 576,906]= 1/86976
Therefore, the GCF of 311/576,678/906 is 1/86976.
To find the highest common factor of 311,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 311 are 1, 311
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 311,678 is 1.
Lets's calculate GCF of 311,678
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 311,678 By Matching Biggest Common Factor Method
Now, list down the factors of 311
:1,311
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 311,678 . The biggest common factor number is the GCF number.
So the greatest common factor 311,678 is 1.
Lets's calculate LCM of 576,906
| 2 | 576, 906 |
| 3 | 288, 453 |
| 96, 151 |
∴ So the LCM of the given numbers is 2 x 3 x 96 x 151 = 86976
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/86976
Therefore, the GCF of Fractions 311/576,678/906 is 1/86976
Least Common Multiple of 576,906 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 576,906 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(576,906) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(576,906) x common factors =6 x 1 = 6
LCM(576,906) = ( 576 × 906 ) / 6
LCM(576,906) = 521856 / 6
LCM(576,906) = 86976
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FAQs on GCF of Fractions of 311/576, 678/906
1. What is the HCF of 311,678?
The HCF of 311,678 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 311/576, 678/906?
Answer: GCF of Numerators as per given numbers 311/576, 678/906 is
GCF of Numerators i.e. for 311,678 is 1
LCM of denominators i.e. for 576,906 is 86976.
Thus, GCF of Fractions is 1/86976.Finally, GCF of Fractions for 311/576, 678/906 is 1/86976.