GCF of 6912/729, 5982/3123
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6912/729, 5982/3123 i.e 6/252963 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6912/729, 5982/3123.
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 6912/729,5982/3123?
Given fractions are 6912/729,5982/3123
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 6912/729,5982/3123, numerators are 6912,5982
Denominators are 729,3123
The GCF of 6912,5982 is 6 .
LCM of 729,3123 is 252963.
The greatest common factor of 6912/729,5982/3123 = [GCF of 6912,5982]/[LCM of 729,3123]= 6/252963
Therefore, the GCF of 6912/729,5982/3123 is 6/252963.
To find the highest common factor of 6912,5982, we have to find the factors of both numbers and list the highest common factor.
The factors of 6912 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 576, 768, 864, 1152, 1728, 2304, 3456, 6912
The factors of 5982 are 1, 2, 3, 6, 997, 1994, 2991, 5982
The HCF of 6912,5982 is 6.
Lets's calculate GCF of 6912,5982
| 2 | 6912, 5982 |
| 3 | 3456, 2991 |
| 1152, 997 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 6912,5982 By Matching Biggest Common Factor Method
Now, list down the factors of 6912
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,64,72,96,108,128,144,192,216,256,288,384,432,576,768,864,1152,1728,2304,3456,6912
Now, list down the factors of 5982
:1,2,3,6,997,1994,2991,5982
Greatest Common Factor
We found the factors 6912,5982 . The biggest common factor number is the GCF number.
So the greatest common factor 6912,5982 is 6.
Lets's calculate LCM of 729,3123
| 3 | 729, 3123 |
| 3 | 243, 1041 |
| 81, 347 |
∴ So the LCM of the given numbers is 3 x 3 x 81 x 347 = 252963
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/252963
Therefore, the GCF of Fractions 6912/729,5982/3123 is 6/252963
Least Common Multiple of 729,3123 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 729,3123 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(729,3123) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(729,3123) x common factors =9 x 1 = 9
LCM(729,3123) = ( 729 × 3123 ) / 9
LCM(729,3123) = 2276667 / 9
LCM(729,3123) = 252963
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 6912/729, 5982/3123
1. What is the HCF of 6912,5982?
The HCF of 6912,5982 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 6912/729, 5982/3123?
Answer: GCF of Numerators as per given numbers 6912/729, 5982/3123 is
GCF of Numerators i.e. for 6912,5982 is 6
LCM of denominators i.e. for 729,3123 is 252963.
Thus, GCF of Fractions is 6/252963.Finally, GCF of Fractions for 6912/729, 5982/3123 is 6/252963.