Use our free GCF of Fractions Calculator tool to compute the GCF of 723/297, 346/684 i.e 1/22572 easily. The following is the detailed procedure to determine the greatest common factor of fractions 723/297, 346/684.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 723/297,346/684
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 723/297,346/684, numerators are 723,346
Denominators are 297,684
The GCF of 723,346 is 1 .
LCM of 297,684 is 22572.
The greatest common factor of 723/297,346/684 = [GCF of 723,346]/[LCM of 297,684]= 1/22572
Therefore, the GCF of 723/297,346/684 is 1/22572.
To find the highest common factor of 723,346, we have to find the factors of both numbers and list the highest common factor.
The factors of 723 are 1, 3, 241, 723
The factors of 346 are 1, 2, 173, 346
The HCF of 723,346 is 1.
Lets's calculate GCF of 723,346
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 723
:1,3,241,723
Now, list down the factors of 346
:1,2,173,346
Greatest Common Factor
We found the factors 723,346 . The biggest common factor number is the GCF number.
So the greatest common factor 723,346 is 1.
Lets's calculate LCM of 297,684
3 | 297, 684 |
3 | 99, 228 |
33, 76 |
∴ So the LCM of the given numbers is 3 x 3 x 33 x 76 = 22572
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/22572
Therefore, the GCF of Fractions 723/297,346/684 is 1/22572
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 297,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(297,684) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(297,684) x common factors =9 x 1 = 9
LCM(297,684) = ( 297 × 684 ) / 9
LCM(297,684) = 203148 / 9
LCM(297,684) = 22572
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 723,346?
The HCF of 723,346 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 723/297, 346/684?
Answer: GCF of Numerators as per given numbers 723/297, 346/684 is
GCF of Numerators i.e. for 723,346 is 1
LCM of denominators i.e. for 297,684 is 22572.
Thus, GCF of Fractions is 1/22572.Finally, GCF of Fractions for 723/297, 346/684 is 1/22572.