GCF of 27/31, 81/45, 186/470
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 27/31, 81/45, 186/470 i.e 3/131130 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/31, 81/45, 186/470.
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 27/31,81/45,186/470?
Given fractions are 27/31,81/45,186/470
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 27/31,81/45,186/470, numerators are 27,81,186
Denominators are 31,45,470
The GCF of 27,81,186 is 3 .
LCM of 31,45,470 is 131130.
The greatest common factor of 27/31,81/45,186/470 = [GCF of 27,81,186]/[LCM of 31,45,470]= 3/131130
Therefore, the GCF of 27/31,81/45,186/470 is 3/131130.
To find the highest common factor of 27,81,186, we have to find the factors of both numbers and list the highest common factor.
The factors of 27 are 1, 3, 9, 27
The factors of 81 are 1, 3, 9, 27, 81
The factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186
The HCF of 27,81,186 is 3.
Lets's calculate GCF of 27,81,186
| 3 | 27, 81, 186 |
| 9, 27, 62 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 27,81,186 By Matching Biggest Common Factor Method
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 81
:1,3,9,27,81
Now, list down the factors of 186
:1,2,3,6,31,62,93,186
Greatest Common Factor
We found the factors 27,81,186 . The biggest common factor number is the GCF number.
So the greatest common factor 27,81,186 is 3.
Lets's calculate LCM of 31,45,470
| 5 | 31, 45, 470 |
| 31, 9, 94 |
∴ So the LCM of the given numbers is 5 x 31 x 9 x 94 = 131130
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/131130
Therefore, the GCF of Fractions 27/31,81/45,186/470 is 3/131130
Least Common Multiple of 31,45,470 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 31,45,470 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,45,470) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(31,45,470) x common factors =1 x 5 = 5
LCM(31,45,470) = ( 31 × 45 × 470 ) / 5
LCM(31,45,470) = 655650 / 5
LCM(31,45,470) = 131130
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 27/31, 81/45, 186/470
1. What is the HCF of 27,81,186?
The HCF of 27,81,186 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 27/31, 81/45, 186/470?
Answer: GCF of Numerators as per given numbers 27/31, 81/45, 186/470 is
GCF of Numerators i.e. for 27,81,186 is 3
LCM of denominators i.e. for 31,45,470 is 131130.
Thus, GCF of Fractions is 3/131130.Finally, GCF of Fractions for 27/31, 81/45, 186/470 is 3/131130.