GCF of 270/414, 9714/431
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 270/414, 9714/431 i.e 6/178434 easily. The following is the detailed procedure to determine the greatest common factor of fractions 270/414, 9714/431.
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 270/414,9714/431?
Given fractions are 270/414,9714/431
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 270/414,9714/431, numerators are 270,9714
Denominators are 414,431
The GCF of 270,9714 is 6 .
LCM of 414,431 is 178434.
The greatest common factor of 270/414,9714/431 = [GCF of 270,9714]/[LCM of 414,431]= 6/178434
Therefore, the GCF of 270/414,9714/431 is 6/178434.
To find the highest common factor of 270,9714, 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 9714 are 1, 2, 3, 6, 1619, 3238, 4857, 9714
The HCF of 270,9714 is 6.
Lets's calculate GCF of 270,9714
| 2 | 270, 9714 |
| 3 | 135, 4857 |
| 45, 1619 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 270,9714 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 9714
:1,2,3,6,1619,3238,4857,9714
Greatest Common Factor
We found the factors 270,9714 . The biggest common factor number is the GCF number.
So the greatest common factor 270,9714 is 6.
Lets's calculate LCM of 414,431
Given numbers has no common factors except 1. So, there LCM is their product i.e 178434
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/178434
Therefore, the GCF of Fractions 270/414,9714/431 is 6/178434
Least Common Multiple of 414,431 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 414,431 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,431) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(414,431) x common factors =1 x 1 = 1
LCM(414,431) = ( 414 × 431 ) / 1
LCM(414,431) = 178434 / 1
LCM(414,431) = 178434
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 270/414, 9714/431
1. What is the HCF of 270,9714?
The HCF of 270,9714 is 6
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 270/414, 9714/431?
Answer: GCF of Numerators as per given numbers 270/414, 9714/431 is
GCF of Numerators i.e. for 270,9714 is 6
LCM of denominators i.e. for 414,431 is 178434.
Thus, GCF of Fractions is 6/178434.Finally, GCF of Fractions for 270/414, 9714/431 is 6/178434.