GCF of 997/51, 564/189
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 997/51, 564/189 i.e 1/3213 easily. The following is the detailed procedure to determine the greatest common factor of fractions 997/51, 564/189.
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 997/51,564/189?
Given fractions are 997/51,564/189
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 997/51,564/189, numerators are 997,564
Denominators are 51,189
The GCF of 997,564 is 1 .
LCM of 51,189 is 3213.
The greatest common factor of 997/51,564/189 = [GCF of 997,564]/[LCM of 51,189]= 1/3213
Therefore, the GCF of 997/51,564/189 is 1/3213.
To find the highest common factor of 997,564, we have to find the factors of both numbers and list the highest common factor.
The factors of 997 are 1, 997
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The HCF of 997,564 is 1.
Lets's calculate GCF of 997,564
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 997,564 By Matching Biggest Common Factor Method
Now, list down the factors of 997
:1,997
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Greatest Common Factor
We found the factors 997,564 . The biggest common factor number is the GCF number.
So the greatest common factor 997,564 is 1.
Lets's calculate LCM of 51,189
| 3 | 51, 189 |
| 17, 63 |
∴ So the LCM of the given numbers is 3 x 17 x 63 = 3213
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3213
Therefore, the GCF of Fractions 997/51,564/189 is 1/3213
Least Common Multiple of 51,189 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 51,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,189) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(51,189) x common factors =3 x 1 = 3
LCM(51,189) = ( 51 × 189 ) / 3
LCM(51,189) = 9639 / 3
LCM(51,189) = 3213
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FAQs on GCF of Fractions of 997/51, 564/189
1. What is the HCF of 997,564?
The HCF of 997,564 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 997/51, 564/189?
Answer: GCF of Numerators as per given numbers 997/51, 564/189 is
GCF of Numerators i.e. for 997,564 is 1
LCM of denominators i.e. for 51,189 is 3213.
Thus, GCF of Fractions is 1/3213.Finally, GCF of Fractions for 997/51, 564/189 is 1/3213.