GCF of 529/81, 108/144
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 529/81, 108/144 i.e 1/1296 easily. The following is the detailed procedure to determine the greatest common factor of fractions 529/81, 108/144.
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 529/81,108/144?
Given fractions are 529/81,108/144
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 529/81,108/144, numerators are 529,108
Denominators are 81,144
The GCF of 529,108 is 1 .
LCM of 81,144 is 1296.
The greatest common factor of 529/81,108/144 = [GCF of 529,108]/[LCM of 81,144]= 1/1296
Therefore, the GCF of 529/81,108/144 is 1/1296.
To find the highest common factor of 529,108, we have to find the factors of both numbers and list the highest common factor.
The factors of 529 are 1, 23, 529
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The HCF of 529,108 is 1.
Lets's calculate GCF of 529,108
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 529,108 By Matching Biggest Common Factor Method
Now, list down the factors of 529
:1,23,529
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Greatest Common Factor
We found the factors 529,108 . The biggest common factor number is the GCF number.
So the greatest common factor 529,108 is 1.
Lets's calculate LCM of 81,144
| 3 | 81, 144 |
| 3 | 27, 48 |
| 9, 16 |
∴ So the LCM of the given numbers is 3 x 3 x 9 x 16 = 1296
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1296
Therefore, the GCF of Fractions 529/81,108/144 is 1/1296
Least Common Multiple of 81,144 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 81,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,144) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(81,144) x common factors =9 x 1 = 9
LCM(81,144) = ( 81 × 144 ) / 9
LCM(81,144) = 11664 / 9
LCM(81,144) = 1296
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FAQs on GCF of Fractions of 529/81, 108/144
1. What is the HCF of 529,108?
The HCF of 529,108 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 529/81, 108/144?
Answer: GCF of Numerators as per given numbers 529/81, 108/144 is
GCF of Numerators i.e. for 529,108 is 1
LCM of denominators i.e. for 81,144 is 1296.
Thus, GCF of Fractions is 1/1296.Finally, GCF of Fractions for 529/81, 108/144 is 1/1296.