GCF of 300/76, 270/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 300/76, 270/214 i.e 30/8132 easily. The following is the detailed procedure to determine the greatest common factor of fractions 300/76, 270/214.
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 300/76,270/214?
Given fractions are 300/76,270/214
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 300/76,270/214, numerators are 300,270
Denominators are 76,214
The GCF of 300,270 is 30 .
LCM of 76,214 is 8132.
The greatest common factor of 300/76,270/214 = [GCF of 300,270]/[LCM of 76,214]= 30/8132
Therefore, the GCF of 300/76,270/214 is 30/8132.
To find the highest common factor of 300,270, we have to find the factors of both numbers and list the highest common factor.
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The HCF of 300,270 is 30.
Lets's calculate GCF of 300,270
| 2 | 300, 270 |
| 3 | 150, 135 |
| 5 | 50, 45 |
| 10, 9 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 300,270 By Matching Biggest Common Factor Method
Now, list down the factors of 300
:1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
Now, list down the factors of 270
:1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270
Greatest Common Factor
We found the factors 300,270 . The biggest common factor number is the GCF number.
So the greatest common factor 300,270 is 30.
Lets's calculate LCM of 76,214
| 2 | 76, 214 |
| 38, 107 |
∴ So the LCM of the given numbers is 2 x 38 x 107 = 8132
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/8132
Therefore, the GCF of Fractions 300/76,270/214 is 30/8132
Least Common Multiple of 76,214 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 76,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(76,214) x common factors =2 x 1 = 2
LCM(76,214) = ( 76 × 214 ) / 2
LCM(76,214) = 16264 / 2
LCM(76,214) = 8132
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FAQs on GCF of Fractions of 300/76, 270/214
1. What is the HCF of 300,270?
The HCF of 300,270 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 300/76, 270/214?
Answer: GCF of Numerators as per given numbers 300/76, 270/214 is
GCF of Numerators i.e. for 300,270 is 30
LCM of denominators i.e. for 76,214 is 8132.
Thus, GCF of Fractions is 30/8132.Finally, GCF of Fractions for 300/76, 270/214 is 30/8132.