GCF of 513/463, 546/578
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 513/463, 546/578 i.e 3/267614 easily. The following is the detailed procedure to determine the greatest common factor of fractions 513/463, 546/578.
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 513/463,546/578?
Given fractions are 513/463,546/578
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 513/463,546/578, numerators are 513,546
Denominators are 463,578
The GCF of 513,546 is 3 .
LCM of 463,578 is 267614.
The greatest common factor of 513/463,546/578 = [GCF of 513,546]/[LCM of 463,578]= 3/267614
Therefore, the GCF of 513/463,546/578 is 3/267614.
To find the highest common factor of 513,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 513,546 is 3.
Lets's calculate GCF of 513,546
| 3 | 513, 546 |
| 171, 182 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 513,546 By Matching Biggest Common Factor Method
Now, list down the factors of 513
:1,3,9,19,27,57,171,513
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Greatest Common Factor
We found the factors 513,546 . The biggest common factor number is the GCF number.
So the greatest common factor 513,546 is 3.
Lets's calculate LCM of 463,578
Given numbers has no common factors except 1. So, there LCM is their product i.e 267614
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/267614
Therefore, the GCF of Fractions 513/463,546/578 is 3/267614
Least Common Multiple of 463,578 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 463,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(463,578) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(463,578) x common factors =1 x 1 = 1
LCM(463,578) = ( 463 × 578 ) / 1
LCM(463,578) = 267614 / 1
LCM(463,578) = 267614
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FAQs on GCF of Fractions of 513/463, 546/578
1. What is the HCF of 513,546?
The HCF of 513,546 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 513/463, 546/578?
Answer: GCF of Numerators as per given numbers 513/463, 546/578 is
GCF of Numerators i.e. for 513,546 is 3
LCM of denominators i.e. for 463,578 is 267614.
Thus, GCF of Fractions is 3/267614.Finally, GCF of Fractions for 513/463, 546/578 is 3/267614.