GCF of 82/284, 30/931, 171/846
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 82/284, 30/931, 171/846 i.e 1/111842892 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/284, 30/931, 171/846.
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 82/284,30/931,171/846?
Given fractions are 82/284,30/931,171/846
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 82/284,30/931,171/846, numerators are 82,30,171
Denominators are 284,931,846
The GCF of 82,30,171 is 1 .
LCM of 284,931,846 is 111842892.
The greatest common factor of 82/284,30/931,171/846 = [GCF of 82,30,171]/[LCM of 284,931,846]= 1/111842892
Therefore, the GCF of 82/284,30/931,171/846 is 1/111842892.
To find the highest common factor of 82,30,171, we have to find the factors of both numbers and list the highest common factor.
The factors of 82 are 1, 2, 41, 82
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 171 are 1, 3, 9, 19, 57, 171
The HCF of 82,30,171 is 1.
Lets's calculate GCF of 82,30,171
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 82,30,171 By Matching Biggest Common Factor Method
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 171
:1,3,9,19,57,171
Greatest Common Factor
We found the factors 82,30,171 . The biggest common factor number is the GCF number.
So the greatest common factor 82,30,171 is 1.
Lets's calculate LCM of 284,931,846
| 2 | 284, 931, 846 |
| 142, 931, 423 |
∴ So the LCM of the given numbers is 2 x 142 x 931 x 423 = 111842892
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/111842892
Therefore, the GCF of Fractions 82/284,30/931,171/846 is 1/111842892
Least Common Multiple of 284,931,846 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 284,931,846 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(284,931,846) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(284,931,846) x common factors =1 x 2 = 2
LCM(284,931,846) = ( 284 × 931 × 846 ) / 2
LCM(284,931,846) = 223685784 / 2
LCM(284,931,846) = 111842892
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FAQs on GCF of Fractions of 82/284, 30/931, 171/846
1. What is the HCF of 82,30,171?
The HCF of 82,30,171 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 82/284, 30/931, 171/846?
Answer: GCF of Numerators as per given numbers 82/284, 30/931, 171/846 is
GCF of Numerators i.e. for 82,30,171 is 1
LCM of denominators i.e. for 284,931,846 is 111842892.
Thus, GCF of Fractions is 1/111842892.Finally, GCF of Fractions for 82/284, 30/931, 171/846 is 1/111842892.