GCF of 75/54, 96/27, 40/240
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 75/54, 96/27, 40/240 i.e 1/2160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/54, 96/27, 40/240.
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 75/54,96/27,40/240?
Given fractions are 75/54,96/27,40/240
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 75/54,96/27,40/240, numerators are 75,96,40
Denominators are 54,27,240
The GCF of 75,96,40 is 1 .
LCM of 54,27,240 is 2160.
The greatest common factor of 75/54,96/27,40/240 = [GCF of 75,96,40]/[LCM of 54,27,240]= 1/2160
Therefore, the GCF of 75/54,96/27,40/240 is 1/2160.
To find the highest common factor of 75,96,40, we have to find the factors of both numbers and list the highest common factor.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The HCF of 75,96,40 is 1.
Lets's calculate GCF of 75,96,40
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 75,96,40 By Matching Biggest Common Factor Method
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Greatest Common Factor
We found the factors 75,96,40 . The biggest common factor number is the GCF number.
So the greatest common factor 75,96,40 is 1.
Lets's calculate LCM of 54,27,240
| 2 | 54, 27, 240 |
| 3 | 27, 27, 120 |
| 3 | 9, 9, 40 |
| 3 | 3, 3, 40 |
| 1, 1, 40 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 1 x 1 x 40 = 2160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2160
Therefore, the GCF of Fractions 75/54,96/27,40/240 is 1/2160
Least Common Multiple of 54,27,240 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 54,27,240 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,27,240) = 3
common factors(in case of two or more numbers have common factors) = 54
GCF(54,27,240) x common factors =3 x 54 = 162
LCM(54,27,240) = ( 54 × 27 × 240 ) / 162
LCM(54,27,240) = 349920 / 162
LCM(54,27,240) = 2160
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FAQs on GCF of Fractions of 75/54, 96/27, 40/240
1. What is the HCF of 75,96,40?
The HCF of 75,96,40 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 75/54, 96/27, 40/240?
Answer: GCF of Numerators as per given numbers 75/54, 96/27, 40/240 is
GCF of Numerators i.e. for 75,96,40 is 1
LCM of denominators i.e. for 54,27,240 is 2160.
Thus, GCF of Fractions is 1/2160.Finally, GCF of Fractions for 75/54, 96/27, 40/240 is 1/2160.