GCF of 270/177, 120/270
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 270/177, 120/270 i.e 30/15930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 270/177, 120/270.
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 270/177,120/270?
Given fractions are 270/177,120/270
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 270/177,120/270, numerators are 270,120
Denominators are 177,270
The GCF of 270,120 is 30 .
LCM of 177,270 is 15930.
The greatest common factor of 270/177,120/270 = [GCF of 270,120]/[LCM of 177,270]= 30/15930
Therefore, the GCF of 270/177,120/270 is 30/15930.
To find the highest common factor of 270,120, 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 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 270,120 is 30.
Lets's calculate GCF of 270,120
| 2 | 270, 120 |
| 3 | 135, 60 |
| 5 | 45, 20 |
| 9, 4 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 270,120 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 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 270,120 . The biggest common factor number is the GCF number.
So the greatest common factor 270,120 is 30.
Lets's calculate LCM of 177,270
| 3 | 177, 270 |
| 59, 90 |
∴ So the LCM of the given numbers is 3 x 59 x 90 = 15930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/15930
Therefore, the GCF of Fractions 270/177,120/270 is 30/15930
Least Common Multiple of 177,270 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 177,270 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(177,270) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(177,270) x common factors =3 x 1 = 3
LCM(177,270) = ( 177 × 270 ) / 3
LCM(177,270) = 47790 / 3
LCM(177,270) = 15930
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FAQs on GCF of Fractions of 270/177, 120/270
1. What is the HCF of 270,120?
The HCF of 270,120 is 30
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 270/177, 120/270?
Answer: GCF of Numerators as per given numbers 270/177, 120/270 is
GCF of Numerators i.e. for 270,120 is 30
LCM of denominators i.e. for 177,270 is 15930.
Thus, GCF of Fractions is 30/15930.Finally, GCF of Fractions for 270/177, 120/270 is 30/15930.