Use our free GCF of Fractions Calculator tool to compute the GCF of 27/66, 415/78, 269/228 i.e 1/32604 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/66, 415/78, 269/228.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 27/66,415/78,269/228
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 27/66,415/78,269/228, numerators are 27,415,269
Denominators are 66,78,228
The GCF of 27,415,269 is 1 .
LCM of 66,78,228 is 32604.
The greatest common factor of 27/66,415/78,269/228 = [GCF of 27,415,269]/[LCM of 66,78,228]= 1/32604
Therefore, the GCF of 27/66,415/78,269/228 is 1/32604.
To find the highest common factor of 27,415,269, 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 415 are 1, 5, 83, 415
The factors of 269 are 1, 269
The HCF of 27,415,269 is 1.
Lets's calculate GCF of 27,415,269
∴ 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 415
:1,5,83,415
Now, list down the factors of 269
:1,269
Greatest Common Factor
We found the factors 27,415,269 . The biggest common factor number is the GCF number.
So the greatest common factor 27,415,269 is 1.
Lets's calculate LCM of 66,78,228
2 | 66, 78, 228 |
3 | 33, 39, 114 |
11, 13, 38 |
∴ So the LCM of the given numbers is 2 x 3 x 11 x 13 x 38 = 32604
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32604
Therefore, the GCF of Fractions 27/66,415/78,269/228 is 1/32604
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 66,78,228 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,78,228) = 6
common factors(in case of two or more numbers have common factors) = 6
GCF(66,78,228) x common factors =6 x 6 = 36
LCM(66,78,228) = ( 66 × 78 × 228 ) / 36
LCM(66,78,228) = 1173744 / 36
LCM(66,78,228) = 32604
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 27,415,269?
The HCF of 27,415,269 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 27/66, 415/78, 269/228?
Answer: GCF of Numerators as per given numbers 27/66, 415/78, 269/228 is
GCF of Numerators i.e. for 27,415,269 is 1
LCM of denominators i.e. for 66,78,228 is 32604.
Thus, GCF of Fractions is 1/32604.Finally, GCF of Fractions for 27/66, 415/78, 269/228 is 1/32604.