GCF of 40/894, 47/108, 314/198
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 40/894, 47/108, 314/198 i.e 1/177012 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/894, 47/108, 314/198.
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 40/894,47/108,314/198?
Given fractions are 40/894,47/108,314/198
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 40/894,47/108,314/198, numerators are 40,47,314
Denominators are 894,108,198
The GCF of 40,47,314 is 1 .
LCM of 894,108,198 is 177012.
The greatest common factor of 40/894,47/108,314/198 = [GCF of 40,47,314]/[LCM of 894,108,198]= 1/177012
Therefore, the GCF of 40/894,47/108,314/198 is 1/177012.
To find the highest common factor of 40,47,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 47 are 1, 47
The factors of 314 are 1, 2, 157, 314
The HCF of 40,47,314 is 1.
Lets's calculate GCF of 40,47,314
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 40,47,314 By Matching Biggest Common Factor Method
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 47
:1,47
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 40,47,314 . The biggest common factor number is the GCF number.
So the greatest common factor 40,47,314 is 1.
Lets's calculate LCM of 894,108,198
| 2 | 894, 108, 198 |
| 3 | 447, 54, 99 |
| 3 | 149, 18, 33 |
| 149, 6, 11 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 149 x 6 x 11 = 177012
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/177012
Therefore, the GCF of Fractions 40/894,47/108,314/198 is 1/177012
Least Common Multiple of 894,108,198 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 894,108,198 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(894,108,198) = 6
common factors(in case of two or more numbers have common factors) = 18
GCF(894,108,198) x common factors =6 x 18 = 108
LCM(894,108,198) = ( 894 × 108 × 198 ) / 108
LCM(894,108,198) = 19117296 / 108
LCM(894,108,198) = 177012
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FAQs on GCF of Fractions of 40/894, 47/108, 314/198
1. What is the HCF of 40,47,314?
The HCF of 40,47,314 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 40/894, 47/108, 314/198?
Answer: GCF of Numerators as per given numbers 40/894, 47/108, 314/198 is
GCF of Numerators i.e. for 40,47,314 is 1
LCM of denominators i.e. for 894,108,198 is 177012.
Thus, GCF of Fractions is 1/177012.Finally, GCF of Fractions for 40/894, 47/108, 314/198 is 1/177012.