GCF of 729/15, 414/544
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 729/15, 414/544 i.e 9/8160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 729/15, 414/544.
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 729/15,414/544?
Given fractions are 729/15,414/544
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 729/15,414/544, numerators are 729,414
Denominators are 15,544
The GCF of 729,414 is 9 .
LCM of 15,544 is 8160.
The greatest common factor of 729/15,414/544 = [GCF of 729,414]/[LCM of 15,544]= 9/8160
Therefore, the GCF of 729/15,414/544 is 9/8160.
To find the highest common factor of 729,414, 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 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 729,414 is 9.
Lets's calculate GCF of 729,414
| 3 | 729, 414 |
| 3 | 243, 138 |
| 81, 46 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 729,414 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 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 729,414 . The biggest common factor number is the GCF number.
So the greatest common factor 729,414 is 9.
Lets's calculate LCM of 15,544
Given numbers has no common factors except 1. So, there LCM is their product i.e 8160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/8160
Therefore, the GCF of Fractions 729/15,414/544 is 9/8160
Least Common Multiple of 15,544 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 15,544 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(15,544) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(15,544) x common factors =1 x 1 = 1
LCM(15,544) = ( 15 × 544 ) / 1
LCM(15,544) = 8160 / 1
LCM(15,544) = 8160
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FAQs on GCF of Fractions of 729/15, 414/544
1. What is the HCF of 729,414?
The HCF of 729,414 is 9
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 729/15, 414/544?
Answer: GCF of Numerators as per given numbers 729/15, 414/544 is
GCF of Numerators i.e. for 729,414 is 9
LCM of denominators i.e. for 15,544 is 8160.
Thus, GCF of Fractions is 9/8160.Finally, GCF of Fractions for 729/15, 414/544 is 9/8160.