GCF of 463/76, 546/319
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 463/76, 546/319 i.e 1/24244 easily. The following is the detailed procedure to determine the greatest common factor of fractions 463/76, 546/319.
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 463/76,546/319?
Given fractions are 463/76,546/319
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 463/76,546/319, numerators are 463,546
Denominators are 76,319
The GCF of 463,546 is 1 .
LCM of 76,319 is 24244.
The greatest common factor of 463/76,546/319 = [GCF of 463,546]/[LCM of 76,319]= 1/24244
Therefore, the GCF of 463/76,546/319 is 1/24244.
To find the highest common factor of 463,546, we have to find the factors of both numbers and list the highest common factor.
The factors of 463 are 1, 463
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The HCF of 463,546 is 1.
Lets's calculate GCF of 463,546
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 463,546 By Matching Biggest Common Factor Method
Now, list down the factors of 463
:1,463
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 463,546 . The biggest common factor number is the GCF number.
So the greatest common factor 463,546 is 1.
Lets's calculate LCM of 76,319
Given numbers has no common factors except 1. So, there LCM is their product i.e 24244
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/24244
Therefore, the GCF of Fractions 463/76,546/319 is 1/24244
Least Common Multiple of 76,319 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 76,319 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,319) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(76,319) x common factors =1 x 1 = 1
LCM(76,319) = ( 76 × 319 ) / 1
LCM(76,319) = 24244 / 1
LCM(76,319) = 24244
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FAQs on GCF of Fractions of 463/76, 546/319
1. What is the HCF of 463,546?
The HCF of 463,546 is 1
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 463/76, 546/319?
Answer: GCF of Numerators as per given numbers 463/76, 546/319 is
GCF of Numerators i.e. for 463,546 is 1
LCM of denominators i.e. for 76,319 is 24244.
Thus, GCF of Fractions is 1/24244.Finally, GCF of Fractions for 463/76, 546/319 is 1/24244.