GCF of 827/18, 102/1898
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 827/18, 102/1898 i.e 1/17082 easily. The following is the detailed procedure to determine the greatest common factor of fractions 827/18, 102/1898.
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 827/18,102/1898?
Given fractions are 827/18,102/1898
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 827/18,102/1898, numerators are 827,102
Denominators are 18,1898
The GCF of 827,102 is 1 .
LCM of 18,1898 is 17082.
The greatest common factor of 827/18,102/1898 = [GCF of 827,102]/[LCM of 18,1898]= 1/17082
Therefore, the GCF of 827/18,102/1898 is 1/17082.
To find the highest common factor of 827,102, we have to find the factors of both numbers and list the highest common factor.
The factors of 827 are 1, 827
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The HCF of 827,102 is 1.
Lets's calculate GCF of 827,102
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 827,102 By Matching Biggest Common Factor Method
Now, list down the factors of 827
:1,827
Now, list down the factors of 102
:1,2,3,6,17,34,51,102
Greatest Common Factor
We found the factors 827,102 . The biggest common factor number is the GCF number.
So the greatest common factor 827,102 is 1.
Lets's calculate LCM of 18,1898
| 2 | 18, 1898 |
| 9, 949 |
∴ So the LCM of the given numbers is 2 x 9 x 949 = 17082
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17082
Therefore, the GCF of Fractions 827/18,102/1898 is 1/17082
Least Common Multiple of 18,1898 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 18,1898 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(18,1898) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(18,1898) x common factors =2 x 1 = 2
LCM(18,1898) = ( 18 × 1898 ) / 2
LCM(18,1898) = 34164 / 2
LCM(18,1898) = 17082
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FAQs on GCF of Fractions of 827/18, 102/1898
1. What is the HCF of 827,102?
The HCF of 827,102 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 827/18, 102/1898?
Answer: GCF of Numerators as per given numbers 827/18, 102/1898 is
GCF of Numerators i.e. for 827,102 is 1
LCM of denominators i.e. for 18,1898 is 17082.
Thus, GCF of Fractions is 1/17082.Finally, GCF of Fractions for 827/18, 102/1898 is 1/17082.