GCF of 729/78, 312/8706
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 729/78, 312/8706 i.e 3/113178 easily. The following is the detailed procedure to determine the greatest common factor of fractions 729/78, 312/8706.
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 729/78,312/8706?
Given fractions are 729/78,312/8706
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 729/78,312/8706, numerators are 729,312
Denominators are 78,8706
The GCF of 729,312 is 3 .
LCM of 78,8706 is 113178.
The greatest common factor of 729/78,312/8706 = [GCF of 729,312]/[LCM of 78,8706]= 3/113178
Therefore, the GCF of 729/78,312/8706 is 3/113178.
To find the highest common factor of 729,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 729 are 1, 3, 9, 27, 81, 243, 729
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 729,312 is 3.
Lets's calculate GCF of 729,312
| 3 | 729, 312 |
| 243, 104 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 729,312 By Matching Biggest Common Factor Method
Now, list down the factors of 729
:1,3,9,27,81,243,729
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 729,312 . The biggest common factor number is the GCF number.
So the greatest common factor 729,312 is 3.
Lets's calculate LCM of 78,8706
| 2 | 78, 8706 |
| 3 | 39, 4353 |
| 13, 1451 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 1451 = 113178
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/113178
Therefore, the GCF of Fractions 729/78,312/8706 is 3/113178
Least Common Multiple of 78,8706 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 78,8706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,8706) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(78,8706) x common factors =6 x 1 = 6
LCM(78,8706) = ( 78 × 8706 ) / 6
LCM(78,8706) = 679068 / 6
LCM(78,8706) = 113178
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FAQs on GCF of Fractions of 729/78, 312/8706
1. What is the HCF of 729,312?
The HCF of 729,312 is 3
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 729/78, 312/8706?
Answer: GCF of Numerators as per given numbers 729/78, 312/8706 is
GCF of Numerators i.e. for 729,312 is 3
LCM of denominators i.e. for 78,8706 is 113178.
Thus, GCF of Fractions is 3/113178.Finally, GCF of Fractions for 729/78, 312/8706 is 3/113178.