GCF of 54/30, 90/75, 108/180
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 54/30, 90/75, 108/180 i.e 18/900 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/30, 90/75, 108/180.
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 54/30,90/75,108/180?
Given fractions are 54/30,90/75,108/180
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 54/30,90/75,108/180, numerators are 54,90,108
Denominators are 30,75,180
The GCF of 54,90,108 is 18 .
LCM of 30,75,180 is 900.
The greatest common factor of 54/30,90/75,108/180 = [GCF of 54,90,108]/[LCM of 30,75,180]= 18/900
Therefore, the GCF of 54/30,90/75,108/180 is 18/900.
To find the highest common factor of 54,90,108, 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 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The HCF of 54,90,108 is 18.
Lets's calculate GCF of 54,90,108
| 2 | 54, 90, 108 |
| 3 | 27, 45, 54 |
| 3 | 9, 15, 18 |
| 3, 5, 6 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 54,90,108 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 108
:1,2,3,4,6,9,12,18,27,36,54,108
Greatest Common Factor
We found the factors 54,90,108 . The biggest common factor number is the GCF number.
So the greatest common factor 54,90,108 is 18.
Lets's calculate LCM of 30,75,180
| 2 | 30, 75, 180 |
| 3 | 15, 75, 90 |
| 5 | 5, 25, 30 |
| 1, 5, 6 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 1 x 5 x 6 = 900
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/900
Therefore, the GCF of Fractions 54/30,90/75,108/180 is 18/900
Least Common Multiple of 30,75,180 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 30,75,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,75,180) = 15
common factors(in case of two or more numbers have common factors) = 30
GCF(30,75,180) x common factors =15 x 30 = 450
LCM(30,75,180) = ( 30 × 75 × 180 ) / 450
LCM(30,75,180) = 405000 / 450
LCM(30,75,180) = 900
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FAQs on GCF of Fractions of 54/30, 90/75, 108/180
1. What is the HCF of 54,90,108?
The HCF of 54,90,108 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 54/30, 90/75, 108/180?
Answer: GCF of Numerators as per given numbers 54/30, 90/75, 108/180 is
GCF of Numerators i.e. for 54,90,108 is 18
LCM of denominators i.e. for 30,75,180 is 900.
Thus, GCF of Fractions is 18/900.Finally, GCF of Fractions for 54/30, 90/75, 108/180 is 18/900.