GCF of 264/408, 729/298
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 264/408, 729/298 i.e 3/60792 easily. The following is the detailed procedure to determine the greatest common factor of fractions 264/408, 729/298.
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 264/408,729/298?
Given fractions are 264/408,729/298
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 264/408,729/298, numerators are 264,729
Denominators are 408,298
The GCF of 264,729 is 3 .
LCM of 408,298 is 60792.
The greatest common factor of 264/408,729/298 = [GCF of 264,729]/[LCM of 408,298]= 3/60792
Therefore, the GCF of 264/408,729/298 is 3/60792.
To find the highest common factor of 264,729, we have to find the factors of both numbers and list the highest common factor.
The factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264
The factors of 729 are 1, 3, 9, 27, 81, 243, 729
The HCF of 264,729 is 3.
Lets's calculate GCF of 264,729
| 3 | 264, 729 |
| 88, 243 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 264,729 By Matching Biggest Common Factor Method
Now, list down the factors of 264
:1,2,3,4,6,8,11,12,22,24,33,44,66,88,132,264
Now, list down the factors of 729
:1,3,9,27,81,243,729
Greatest Common Factor
We found the factors 264,729 . The biggest common factor number is the GCF number.
So the greatest common factor 264,729 is 3.
Lets's calculate LCM of 408,298
| 2 | 408, 298 |
| 204, 149 |
∴ So the LCM of the given numbers is 2 x 204 x 149 = 60792
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/60792
Therefore, the GCF of Fractions 264/408,729/298 is 3/60792
Least Common Multiple of 408,298 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 408,298 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(408,298) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(408,298) x common factors =2 x 1 = 2
LCM(408,298) = ( 408 × 298 ) / 2
LCM(408,298) = 121584 / 2
LCM(408,298) = 60792
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FAQs on GCF of Fractions of 264/408, 729/298
1. What is the HCF of 264,729?
The HCF of 264,729 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 264/408, 729/298?
Answer: GCF of Numerators as per given numbers 264/408, 729/298 is
GCF of Numerators i.e. for 264,729 is 3
LCM of denominators i.e. for 408,298 is 60792.
Thus, GCF of Fractions is 3/60792.Finally, GCF of Fractions for 264/408, 729/298 is 3/60792.