Use our free GCF of Fractions Calculator tool to compute the GCF of 192/349, 438/620 i.e 6/216380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 192/349, 438/620.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 192/349,438/620
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 192/349,438/620, numerators are 192,438
Denominators are 349,620
The GCF of 192,438 is 6 .
LCM of 349,620 is 216380.
The greatest common factor of 192/349,438/620 = [GCF of 192,438]/[LCM of 349,620]= 6/216380
Therefore, the GCF of 192/349,438/620 is 6/216380.
To find the highest common factor of 192,438, we have to find the factors of both numbers and list the highest common factor.
The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
The factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438
The HCF of 192,438 is 6.
Lets's calculate GCF of 192,438
2 | 192, 438 |
3 | 96, 219 |
32, 73 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 192
:1,2,3,4,6,8,12,16,24,32,48,64,96,192
Now, list down the factors of 438
:1,2,3,6,73,146,219,438
Greatest Common Factor
We found the factors 192,438 . The biggest common factor number is the GCF number.
So the greatest common factor 192,438 is 6.
Lets's calculate LCM of 349,620
Given numbers has no common factors except 1. So, there LCM is their product i.e 216380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/216380
Therefore, the GCF of Fractions 192/349,438/620 is 6/216380
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 349,620 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(349,620) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(349,620) x common factors =1 x 1 = 1
LCM(349,620) = ( 349 × 620 ) / 1
LCM(349,620) = 216380 / 1
LCM(349,620) = 216380
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 192,438?
The HCF of 192,438 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 192/349, 438/620?
Answer: GCF of Numerators as per given numbers 192/349, 438/620 is
GCF of Numerators i.e. for 192,438 is 6
LCM of denominators i.e. for 349,620 is 216380.
Thus, GCF of Fractions is 6/216380.Finally, GCF of Fractions for 192/349, 438/620 is 6/216380.