Use our free GCF of Fractions Calculator tool to compute the GCF of 74/192, 42/623, 589/684 i.e 1/6818112 easily. The following is the detailed procedure to determine the greatest common factor of fractions 74/192, 42/623, 589/684.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 74/192,42/623,589/684
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 74/192,42/623,589/684, numerators are 74,42,589
Denominators are 192,623,684
The GCF of 74,42,589 is 1 .
LCM of 192,623,684 is 6818112.
The greatest common factor of 74/192,42/623,589/684 = [GCF of 74,42,589]/[LCM of 192,623,684]= 1/6818112
Therefore, the GCF of 74/192,42/623,589/684 is 1/6818112.
To find the highest common factor of 74,42,589, we have to find the factors of both numbers and list the highest common factor.
The factors of 74 are 1, 2, 37, 74
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 589 are 1, 19, 31, 589
The HCF of 74,42,589 is 1.
Lets's calculate GCF of 74,42,589
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 589
:1,19,31,589
Greatest Common Factor
We found the factors 74,42,589 . The biggest common factor number is the GCF number.
So the greatest common factor 74,42,589 is 1.
Lets's calculate LCM of 192,623,684
2 | 192, 623, 684 |
2 | 96, 623, 342 |
3 | 48, 623, 171 |
16, 623, 57 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 16 x 623 x 57 = 6818112
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6818112
Therefore, the GCF of Fractions 74/192,42/623,589/684 is 1/6818112
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 192,623,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(192,623,684) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(192,623,684) x common factors =1 x 12 = 12
LCM(192,623,684) = ( 192 × 623 × 684 ) / 12
LCM(192,623,684) = 81817344 / 12
LCM(192,623,684) = 6818112
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 74,42,589?
The HCF of 74,42,589 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 74/192, 42/623, 589/684?
Answer: GCF of Numerators as per given numbers 74/192, 42/623, 589/684 is
GCF of Numerators i.e. for 74,42,589 is 1
LCM of denominators i.e. for 192,623,684 is 6818112.
Thus, GCF of Fractions is 1/6818112.Finally, GCF of Fractions for 74/192, 42/623, 589/684 is 1/6818112.