GCF of 114/27, 380/927
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 114/27, 380/927 i.e 38/2781 easily. The following is the detailed procedure to determine the greatest common factor of fractions 114/27, 380/927.
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 114/27,380/927?
Given fractions are 114/27,380/927
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 114/27,380/927, numerators are 114,380
Denominators are 27,927
The GCF of 114,380 is 38 .
LCM of 27,927 is 2781.
The greatest common factor of 114/27,380/927 = [GCF of 114,380]/[LCM of 27,927]= 38/2781
Therefore, the GCF of 114/27,380/927 is 38/2781.
To find the highest common factor of 114,380, we have to find the factors of both numbers and list the highest common factor.
The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114
The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
The HCF of 114,380 is 38.
Lets's calculate GCF of 114,380
| 2 | 114, 380 |
| 19 | 57, 190 |
| 3, 10 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 114,380 By Matching Biggest Common Factor Method
Now, list down the factors of 114
:1,2,3,6,19,38,57,114
Now, list down the factors of 380
:1,2,4,5,10,19,20,38,76,95,190,380
Greatest Common Factor
We found the factors 114,380 . The biggest common factor number is the GCF number.
So the greatest common factor 114,380 is 38.
Lets's calculate LCM of 27,927
| 3 | 27, 927 |
| 3 | 9, 309 |
| 3, 103 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 103 = 2781
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/2781
Therefore, the GCF of Fractions 114/27,380/927 is 38/2781
Least Common Multiple of 27,927 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 27,927 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,927) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(27,927) x common factors =9 x 1 = 9
LCM(27,927) = ( 27 × 927 ) / 9
LCM(27,927) = 25029 / 9
LCM(27,927) = 2781
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 114/27, 380/927
1. What is the HCF of 114,380?
The HCF of 114,380 is 38
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 114/27, 380/927?
Answer: GCF of Numerators as per given numbers 114/27, 380/927 is
GCF of Numerators i.e. for 114,380 is 38
LCM of denominators i.e. for 27,927 is 2781.
Thus, GCF of Fractions is 38/2781.Finally, GCF of Fractions for 114/27, 380/927 is 38/2781.