Use our free GCF of Fractions Calculator tool to compute the GCF of 138/731, 384/102 i.e 6/4386 easily. The following is the detailed procedure to determine the greatest common factor of fractions 138/731, 384/102.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 138/731,384/102
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 138/731,384/102, numerators are 138,384
Denominators are 731,102
The GCF of 138,384 is 6 .
LCM of 731,102 is 4386.
The greatest common factor of 138/731,384/102 = [GCF of 138,384]/[LCM of 731,102]= 6/4386
Therefore, the GCF of 138/731,384/102 is 6/4386.
To find the highest common factor of 138,384, we have to find the factors of both numbers and list the highest common factor.
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The HCF of 138,384 is 6.
Lets's calculate GCF of 138,384
2 | 138, 384 |
3 | 69, 192 |
23, 64 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Greatest Common Factor
We found the factors 138,384 . The biggest common factor number is the GCF number.
So the greatest common factor 138,384 is 6.
Lets's calculate LCM of 731,102
17 | 731, 102 |
43, 6 |
∴ So the LCM of the given numbers is 17 x 43 x 6 = 4386
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/4386
Therefore, the GCF of Fractions 138/731,384/102 is 6/4386
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 731,102 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(731,102) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(731,102) x common factors =17 x 1 = 17
LCM(731,102) = ( 731 × 102 ) / 17
LCM(731,102) = 74562 / 17
LCM(731,102) = 4386
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 138,384?
The HCF of 138,384 is 6
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 138/731, 384/102?
Answer: GCF of Numerators as per given numbers 138/731, 384/102 is
GCF of Numerators i.e. for 138,384 is 6
LCM of denominators i.e. for 731,102 is 4386.
Thus, GCF of Fractions is 6/4386.Finally, GCF of Fractions for 138/731, 384/102 is 6/4386.