Use our free GCF of Fractions Calculator tool to compute the GCF of 27/361, 85/205, 812/265 i.e 1/3922265 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/361, 85/205, 812/265.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 27/361,85/205,812/265
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 27/361,85/205,812/265, numerators are 27,85,812
Denominators are 361,205,265
The GCF of 27,85,812 is 1 .
LCM of 361,205,265 is 3922265.
The greatest common factor of 27/361,85/205,812/265 = [GCF of 27,85,812]/[LCM of 361,205,265]= 1/3922265
Therefore, the GCF of 27/361,85/205,812/265 is 1/3922265.
To find the highest common factor of 27,85,812, 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 85 are 1, 5, 17, 85
The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
The HCF of 27,85,812 is 1.
Lets's calculate GCF of 27,85,812
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 85
:1,5,17,85
Now, list down the factors of 812
:1,2,4,7,14,28,29,58,116,203,406,812
Greatest Common Factor
We found the factors 27,85,812 . The biggest common factor number is the GCF number.
So the greatest common factor 27,85,812 is 1.
Lets's calculate LCM of 361,205,265
5 | 361, 205, 265 |
361, 41, 53 |
∴ So the LCM of the given numbers is 5 x 361 x 41 x 53 = 3922265
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3922265
Therefore, the GCF of Fractions 27/361,85/205,812/265 is 1/3922265
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 361,205,265 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(361,205,265) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(361,205,265) x common factors =1 x 5 = 5
LCM(361,205,265) = ( 361 × 205 × 265 ) / 5
LCM(361,205,265) = 19611325 / 5
LCM(361,205,265) = 3922265
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 27,85,812?
The HCF of 27,85,812 is 1
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 27/361, 85/205, 812/265?
Answer: GCF of Numerators as per given numbers 27/361, 85/205, 812/265 is
GCF of Numerators i.e. for 27,85,812 is 1
LCM of denominators i.e. for 361,205,265 is 3922265.
Thus, GCF of Fractions is 1/3922265.Finally, GCF of Fractions for 27/361, 85/205, 812/265 is 1/3922265.