Use our free GCF of Fractions Calculator tool to compute the GCF of 123/188, 670/446 i.e 1/41924 easily. The following is the detailed procedure to determine the greatest common factor of fractions 123/188, 670/446.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 123/188,670/446
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 123/188,670/446, numerators are 123,670
Denominators are 188,446
The GCF of 123,670 is 1 .
LCM of 188,446 is 41924.
The greatest common factor of 123/188,670/446 = [GCF of 123,670]/[LCM of 188,446]= 1/41924
Therefore, the GCF of 123/188,670/446 is 1/41924.
To find the highest common factor of 123,670, we have to find the factors of both numbers and list the highest common factor.
The factors of 123 are 1, 3, 41, 123
The factors of 670 are 1, 2, 5, 10, 67, 134, 335, 670
The HCF of 123,670 is 1.
Lets's calculate GCF of 123,670
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 123
:1,3,41,123
Now, list down the factors of 670
:1,2,5,10,67,134,335,670
Greatest Common Factor
We found the factors 123,670 . The biggest common factor number is the GCF number.
So the greatest common factor 123,670 is 1.
Lets's calculate LCM of 188,446
2 | 188, 446 |
94, 223 |
∴ So the LCM of the given numbers is 2 x 94 x 223 = 41924
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/41924
Therefore, the GCF of Fractions 123/188,670/446 is 1/41924
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 188,446 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(188,446) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(188,446) x common factors =2 x 1 = 2
LCM(188,446) = ( 188 × 446 ) / 2
LCM(188,446) = 83848 / 2
LCM(188,446) = 41924
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 123,670?
The HCF of 123,670 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 123/188, 670/446?
Answer: GCF of Numerators as per given numbers 123/188, 670/446 is
GCF of Numerators i.e. for 123,670 is 1
LCM of denominators i.e. for 188,446 is 41924.
Thus, GCF of Fractions is 1/41924.Finally, GCF of Fractions for 123/188, 670/446 is 1/41924.