GCF of 461/728, 512/114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 461/728, 512/114 i.e 1/41496 easily. The following is the detailed procedure to determine the greatest common factor of fractions 461/728, 512/114.
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 461/728,512/114?
Given fractions are 461/728,512/114
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 461/728,512/114, numerators are 461,512
Denominators are 728,114
The GCF of 461,512 is 1 .
LCM of 728,114 is 41496.
The greatest common factor of 461/728,512/114 = [GCF of 461,512]/[LCM of 728,114]= 1/41496
Therefore, the GCF of 461/728,512/114 is 1/41496.
To find the highest common factor of 461,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 461 are 1, 461
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 461,512 is 1.
Lets's calculate GCF of 461,512
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 461,512 By Matching Biggest Common Factor Method
Now, list down the factors of 461
:1,461
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 461,512 . The biggest common factor number is the GCF number.
So the greatest common factor 461,512 is 1.
Lets's calculate LCM of 728,114
| 2 | 728, 114 |
| 364, 57 |
∴ So the LCM of the given numbers is 2 x 364 x 57 = 41496
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/41496
Therefore, the GCF of Fractions 461/728,512/114 is 1/41496
Least Common Multiple of 728,114 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 728,114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(728,114) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(728,114) x common factors =2 x 1 = 2
LCM(728,114) = ( 728 × 114 ) / 2
LCM(728,114) = 82992 / 2
LCM(728,114) = 41496
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FAQs on GCF of Fractions of 461/728, 512/114
1. What is the HCF of 461,512?
The HCF of 461,512 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 461/728, 512/114?
Answer: GCF of Numerators as per given numbers 461/728, 512/114 is
GCF of Numerators i.e. for 461,512 is 1
LCM of denominators i.e. for 728,114 is 41496.
Thus, GCF of Fractions is 1/41496.Finally, GCF of Fractions for 461/728, 512/114 is 1/41496.