GCF of 54/309, 90/590, 144/611
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 54/309, 90/590, 144/611 i.e 18/111391410 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/309, 90/590, 144/611.
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 54/309,90/590,144/611?
Given fractions are 54/309,90/590,144/611
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 54/309,90/590,144/611, numerators are 54,90,144
Denominators are 309,590,611
The GCF of 54,90,144 is 18 .
LCM of 309,590,611 is 111391410.
The greatest common factor of 54/309,90/590,144/611 = [GCF of 54,90,144]/[LCM of 309,590,611]= 18/111391410
Therefore, the GCF of 54/309,90/590,144/611 is 18/111391410.
To find the highest common factor of 54,90,144, we have to find the factors of both numbers and list the highest common factor.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The HCF of 54,90,144 is 18.
Lets's calculate GCF of 54,90,144
| 2 | 54, 90, 144 |
| 3 | 27, 45, 72 |
| 3 | 9, 15, 24 |
| 3, 5, 8 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 54,90,144 By Matching Biggest Common Factor Method
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 90
:1,2,3,5,6,9,10,15,18,30,45,90
Now, list down the factors of 144
:1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
Greatest Common Factor
We found the factors 54,90,144 . The biggest common factor number is the GCF number.
So the greatest common factor 54,90,144 is 18.
Lets's calculate LCM of 309,590,611
Given numbers has no common factors except 1. So, there LCM is their product i.e 111391410
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/111391410
Therefore, the GCF of Fractions 54/309,90/590,144/611 is 18/111391410
Least Common Multiple of 309,590,611 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 309,590,611 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,590,611) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(309,590,611) x common factors =1 x 1 = 1
LCM(309,590,611) = ( 309 × 590 × 611 ) / 1
LCM(309,590,611) = 111391410 / 1
LCM(309,590,611) = 111391410
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FAQs on GCF of Fractions of 54/309, 90/590, 144/611
1. What is the HCF of 54,90,144?
The HCF of 54,90,144 is 18
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 54/309, 90/590, 144/611?
Answer: GCF of Numerators as per given numbers 54/309, 90/590, 144/611 is
GCF of Numerators i.e. for 54,90,144 is 18
LCM of denominators i.e. for 309,590,611 is 111391410.
Thus, GCF of Fractions is 18/111391410.Finally, GCF of Fractions for 54/309, 90/590, 144/611 is 18/111391410.