Use our free GCF of Fractions Calculator tool to compute the GCF of 188/178, 428/314 i.e 4/27946 easily. The following is the detailed procedure to determine the greatest common factor of fractions 188/178, 428/314.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 188/178,428/314
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 188/178,428/314, numerators are 188,428
Denominators are 178,314
The GCF of 188,428 is 4 .
LCM of 178,314 is 27946.
The greatest common factor of 188/178,428/314 = [GCF of 188,428]/[LCM of 178,314]= 4/27946
Therefore, the GCF of 188/178,428/314 is 4/27946.
To find the highest common factor of 188,428, we have to find the factors of both numbers and list the highest common factor.
The factors of 188 are 1, 2, 4, 47, 94, 188
The factors of 428 are 1, 2, 4, 107, 214, 428
The HCF of 188,428 is 4.
Lets's calculate GCF of 188,428
2 | 188, 428 |
2 | 94, 214 |
47, 107 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 188
:1,2,4,47,94,188
Now, list down the factors of 428
:1,2,4,107,214,428
Greatest Common Factor
We found the factors 188,428 . The biggest common factor number is the GCF number.
So the greatest common factor 188,428 is 4.
Lets's calculate LCM of 178,314
2 | 178, 314 |
89, 157 |
∴ So the LCM of the given numbers is 2 x 89 x 157 = 27946
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/27946
Therefore, the GCF of Fractions 188/178,428/314 is 4/27946
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 178,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(178,314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(178,314) x common factors =2 x 1 = 2
LCM(178,314) = ( 178 × 314 ) / 2
LCM(178,314) = 55892 / 2
LCM(178,314) = 27946
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 188,428?
The HCF of 188,428 is 4
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 188/178, 428/314?
Answer: GCF of Numerators as per given numbers 188/178, 428/314 is
GCF of Numerators i.e. for 188,428 is 4
LCM of denominators i.e. for 178,314 is 27946.
Thus, GCF of Fractions is 4/27946.Finally, GCF of Fractions for 188/178, 428/314 is 4/27946.