Use our free GCF of Fractions Calculator tool to compute the GCF of 60/338, 23/468, 469/204 i.e 1/103428 easily. The following is the detailed procedure to determine the greatest common factor of fractions 60/338, 23/468, 469/204.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 60/338,23/468,469/204
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 60/338,23/468,469/204, numerators are 60,23,469
Denominators are 338,468,204
The GCF of 60,23,469 is 1 .
LCM of 338,468,204 is 103428.
The greatest common factor of 60/338,23/468,469/204 = [GCF of 60,23,469]/[LCM of 338,468,204]= 1/103428
Therefore, the GCF of 60/338,23/468,469/204 is 1/103428.
To find the highest common factor of 60,23,469, we have to find the factors of both numbers and list the highest common factor.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 23 are 1, 23
The factors of 469 are 1, 7, 67, 469
The HCF of 60,23,469 is 1.
Lets's calculate GCF of 60,23,469
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Now, list down the factors of 23
:1,23
Now, list down the factors of 469
:1,7,67,469
Greatest Common Factor
We found the factors 60,23,469 . The biggest common factor number is the GCF number.
So the greatest common factor 60,23,469 is 1.
Lets's calculate LCM of 338,468,204
2 | 338, 468, 204 |
2 | 169, 234, 102 |
3 | 169, 117, 51 |
13 | 169, 39, 17 |
13, 3, 17 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 13 x 3 x 17 = 103428
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/103428
Therefore, the GCF of Fractions 60/338,23/468,469/204 is 1/103428
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 338,468,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(338,468,204) = 2
common factors(in case of two or more numbers have common factors) = 156
GCF(338,468,204) x common factors =2 x 156 = 312
LCM(338,468,204) = ( 338 × 468 × 204 ) / 312
LCM(338,468,204) = 32269536 / 312
LCM(338,468,204) = 103428
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 60,23,469?
The HCF of 60,23,469 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 60/338, 23/468, 469/204?
Answer: GCF of Numerators as per given numbers 60/338, 23/468, 469/204 is
GCF of Numerators i.e. for 60,23,469 is 1
LCM of denominators i.e. for 338,468,204 is 103428.
Thus, GCF of Fractions is 1/103428.Finally, GCF of Fractions for 60/338, 23/468, 469/204 is 1/103428.