Use our free GCF of Fractions Calculator tool to compute the GCF of 27/803, 21/284, 906/176 i.e 3/912208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/803, 21/284, 906/176.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 27/803,21/284,906/176
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 27/803,21/284,906/176, numerators are 27,21,906
Denominators are 803,284,176
The GCF of 27,21,906 is 3 .
LCM of 803,284,176 is 912208.
The greatest common factor of 27/803,21/284,906/176 = [GCF of 27,21,906]/[LCM of 803,284,176]= 3/912208
Therefore, the GCF of 27/803,21/284,906/176 is 3/912208.
To find the highest common factor of 27,21,906, 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 21 are 1, 3, 7, 21
The factors of 906 are 1, 2, 3, 6, 151, 302, 453, 906
The HCF of 27,21,906 is 3.
Lets's calculate GCF of 27,21,906
3 | 27, 21, 906 |
9, 7, 302 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 906
:1,2,3,6,151,302,453,906
Greatest Common Factor
We found the factors 27,21,906 . The biggest common factor number is the GCF number.
So the greatest common factor 27,21,906 is 3.
Lets's calculate LCM of 803,284,176
2 | 803, 284, 176 |
2 | 803, 142, 88 |
11 | 803, 71, 44 |
73, 71, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 11 x 73 x 71 x 4 = 912208
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/912208
Therefore, the GCF of Fractions 27/803,21/284,906/176 is 3/912208
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 803,284,176 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(803,284,176) = 1
common factors(in case of two or more numbers have common factors) = 44
GCF(803,284,176) x common factors =1 x 44 = 44
LCM(803,284,176) = ( 803 × 284 × 176 ) / 44
LCM(803,284,176) = 40137152 / 44
LCM(803,284,176) = 912208
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 27,21,906?
The HCF of 27,21,906 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 27/803, 21/284, 906/176?
Answer: GCF of Numerators as per given numbers 27/803, 21/284, 906/176 is
GCF of Numerators i.e. for 27,21,906 is 3
LCM of denominators i.e. for 803,284,176 is 912208.
Thus, GCF of Fractions is 3/912208.Finally, GCF of Fractions for 27/803, 21/284, 906/176 is 3/912208.