GCF of 270/192, 249/280
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 270/192, 249/280 i.e 3/6720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 270/192, 249/280.
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 270/192,249/280?
Given fractions are 270/192,249/280
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 270/192,249/280, numerators are 270,249
Denominators are 192,280
The GCF of 270,249 is 3 .
LCM of 192,280 is 6720.
The greatest common factor of 270/192,249/280 = [GCF of 270,249]/[LCM of 192,280]= 3/6720
Therefore, the GCF of 270/192,249/280 is 3/6720.
To find the highest common factor of 270,249, we have to find the factors of both numbers and list the highest common factor.
The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The factors of 249 are 1, 3, 83, 249
The HCF of 270,249 is 3.
Lets's calculate GCF of 270,249
| 3 | 270, 249 |
| 90, 83 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 270,249 By Matching Biggest Common Factor Method
Now, list down the factors of 270
:1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270
Now, list down the factors of 249
:1,3,83,249
Greatest Common Factor
We found the factors 270,249 . The biggest common factor number is the GCF number.
So the greatest common factor 270,249 is 3.
Lets's calculate LCM of 192,280
| 2 | 192, 280 |
| 2 | 96, 140 |
| 2 | 48, 70 |
| 24, 35 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 24 x 35 = 6720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/6720
Therefore, the GCF of Fractions 270/192,249/280 is 3/6720
Least Common Multiple of 192,280 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 192,280 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(192,280) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(192,280) x common factors =8 x 1 = 8
LCM(192,280) = ( 192 × 280 ) / 8
LCM(192,280) = 53760 / 8
LCM(192,280) = 6720
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FAQs on GCF of Fractions of 270/192, 249/280
1. What is the HCF of 270,249?
The HCF of 270,249 is 3
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 270/192, 249/280?
Answer: GCF of Numerators as per given numbers 270/192, 249/280 is
GCF of Numerators i.e. for 270,249 is 3
LCM of denominators i.e. for 192,280 is 6720.
Thus, GCF of Fractions is 3/6720.Finally, GCF of Fractions for 270/192, 249/280 is 3/6720.