GCF of 97/81, 21/38, 321/189
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 97/81, 21/38, 321/189 i.e 1/21546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 97/81, 21/38, 321/189.
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 97/81,21/38,321/189?
Given fractions are 97/81,21/38,321/189
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 97/81,21/38,321/189, numerators are 97,21,321
Denominators are 81,38,189
The GCF of 97,21,321 is 1 .
LCM of 81,38,189 is 21546.
The greatest common factor of 97/81,21/38,321/189 = [GCF of 97,21,321]/[LCM of 81,38,189]= 1/21546
Therefore, the GCF of 97/81,21/38,321/189 is 1/21546.
To find the highest common factor of 97,21,321, we have to find the factors of both numbers and list the highest common factor.
The factors of 97 are 1, 97
The factors of 21 are 1, 3, 7, 21
The factors of 321 are 1, 3, 107, 321
The HCF of 97,21,321 is 1.
Lets's calculate GCF of 97,21,321
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 97,21,321 By Matching Biggest Common Factor Method
Now, list down the factors of 97
:1,97
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 321
:1,3,107,321
Greatest Common Factor
We found the factors 97,21,321 . The biggest common factor number is the GCF number.
So the greatest common factor 97,21,321 is 1.
Lets's calculate LCM of 81,38,189
| 3 | 81, 38, 189 |
| 3 | 27, 38, 63 |
| 3 | 9, 38, 21 |
| 3, 38, 7 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 3 x 38 x 7 = 21546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/21546
Therefore, the GCF of Fractions 97/81,21/38,321/189 is 1/21546
Least Common Multiple of 81,38,189 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 81,38,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,38,189) = 1
common factors(in case of two or more numbers have common factors) = 27
GCF(81,38,189) x common factors =1 x 27 = 27
LCM(81,38,189) = ( 81 × 38 × 189 ) / 27
LCM(81,38,189) = 581742 / 27
LCM(81,38,189) = 21546
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FAQs on GCF of Fractions of 97/81, 21/38, 321/189
1. What is the HCF of 97,21,321?
The HCF of 97,21,321 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 97/81, 21/38, 321/189?
Answer: GCF of Numerators as per given numbers 97/81, 21/38, 321/189 is
GCF of Numerators i.e. for 97,21,321 is 1
LCM of denominators i.e. for 81,38,189 is 21546.
Thus, GCF of Fractions is 1/21546.Finally, GCF of Fractions for 97/81, 21/38, 321/189 is 1/21546.