Use our free GCF of Fractions Calculator tool to compute the GCF of 27/384, 609/508, 654/781 i.e 3/38087808 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/384, 609/508, 654/781.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 27/384,609/508,654/781
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 27/384,609/508,654/781, numerators are 27,609,654
Denominators are 384,508,781
The GCF of 27,609,654 is 3 .
LCM of 384,508,781 is 38087808.
The greatest common factor of 27/384,609/508,654/781 = [GCF of 27,609,654]/[LCM of 384,508,781]= 3/38087808
Therefore, the GCF of 27/384,609/508,654/781 is 3/38087808.
To find the highest common factor of 27,609,654, 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 609 are 1, 3, 7, 21, 29, 87, 203, 609
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The HCF of 27,609,654 is 3.
Lets's calculate GCF of 27,609,654
3 | 27, 609, 654 |
9, 203, 218 |
∴ 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 609
:1,3,7,21,29,87,203,609
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Greatest Common Factor
We found the factors 27,609,654 . The biggest common factor number is the GCF number.
So the greatest common factor 27,609,654 is 3.
Lets's calculate LCM of 384,508,781
2 | 384, 508, 781 |
2 | 192, 254, 781 |
96, 127, 781 |
∴ So the LCM of the given numbers is 2 x 2 x 96 x 127 x 781 = 38087808
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/38087808
Therefore, the GCF of Fractions 27/384,609/508,654/781 is 3/38087808
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 384,508,781 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(384,508,781) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(384,508,781) x common factors =1 x 4 = 4
LCM(384,508,781) = ( 384 × 508 × 781 ) / 4
LCM(384,508,781) = 152351232 / 4
LCM(384,508,781) = 38087808
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 27,609,654?
The HCF of 27,609,654 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 27/384, 609/508, 654/781?
Answer: GCF of Numerators as per given numbers 27/384, 609/508, 654/781 is
GCF of Numerators i.e. for 27,609,654 is 3
LCM of denominators i.e. for 384,508,781 is 38087808.
Thus, GCF of Fractions is 3/38087808.Finally, GCF of Fractions for 27/384, 609/508, 654/781 is 3/38087808.