GCF of 196/723, 777/729
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 196/723, 777/729 i.e 7/175689 easily. The following is the detailed procedure to determine the greatest common factor of fractions 196/723, 777/729.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 196/723,777/729?
Given fractions are 196/723,777/729
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 196/723,777/729, numerators are 196,777
Denominators are 723,729
The GCF of 196,777 is 7 .
LCM of 723,729 is 175689.
The greatest common factor of 196/723,777/729 = [GCF of 196,777]/[LCM of 723,729]= 7/175689
Therefore, the GCF of 196/723,777/729 is 7/175689.
To find the highest common factor of 196,777, we have to find the factors of both numbers and list the highest common factor.
The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196
The factors of 777 are 1, 3, 7, 21, 37, 111, 259, 777
The HCF of 196,777 is 7.
Lets's calculate GCF of 196,777
| 7 | 196, 777 |
| 28, 111 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 196,777 By Matching Biggest Common Factor Method
Now, list down the factors of 196
:1,2,4,7,14,28,49,98,196
Now, list down the factors of 777
:1,3,7,21,37,111,259,777
Greatest Common Factor
We found the factors 196,777 . The biggest common factor number is the GCF number.
So the greatest common factor 196,777 is 7.
Lets's calculate LCM of 723,729
| 3 | 723, 729 |
| 241, 243 |
∴ So the LCM of the given numbers is 3 x 241 x 243 = 175689
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/175689
Therefore, the GCF of Fractions 196/723,777/729 is 7/175689
Least Common Multiple of 723,729 with GCF Formula
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 723,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(723,729) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(723,729) x common factors =3 x 1 = 3
LCM(723,729) = ( 723 × 729 ) / 3
LCM(723,729) = 527067 / 3
LCM(723,729) = 175689
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FAQs on GCF of Fractions of 196/723, 777/729
1. What is the HCF of 196,777?
The HCF of 196,777 is 7
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 196/723, 777/729?
Answer: GCF of Numerators as per given numbers 196/723, 777/729 is
GCF of Numerators i.e. for 196,777 is 7
LCM of denominators i.e. for 723,729 is 175689.
Thus, GCF of Fractions is 7/175689.Finally, GCF of Fractions for 196/723, 777/729 is 7/175689.