GCF of 728/30, 512/418
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 728/30, 512/418 i.e 8/6270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/30, 512/418.
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 728/30,512/418?
Given fractions are 728/30,512/418
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 728/30,512/418, numerators are 728,512
Denominators are 30,418
The GCF of 728,512 is 8 .
LCM of 30,418 is 6270.
The greatest common factor of 728/30,512/418 = [GCF of 728,512]/[LCM of 30,418]= 8/6270
Therefore, the GCF of 728/30,512/418 is 8/6270.
To find the highest common factor of 728,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 728,512 is 8.
Lets's calculate GCF of 728,512
| 2 | 728, 512 |
| 2 | 364, 256 |
| 2 | 182, 128 |
| 91, 64 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 728,512 By Matching Biggest Common Factor Method
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 728,512 . The biggest common factor number is the GCF number.
So the greatest common factor 728,512 is 8.
Lets's calculate LCM of 30,418
| 2 | 30, 418 |
| 15, 209 |
∴ So the LCM of the given numbers is 2 x 15 x 209 = 6270
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/6270
Therefore, the GCF of Fractions 728/30,512/418 is 8/6270
Least Common Multiple of 30,418 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 30,418 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,418) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(30,418) x common factors =2 x 1 = 2
LCM(30,418) = ( 30 × 418 ) / 2
LCM(30,418) = 12540 / 2
LCM(30,418) = 6270
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 728/30, 512/418
1. What is the HCF of 728,512?
The HCF of 728,512 is 8
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 728/30, 512/418?
Answer: GCF of Numerators as per given numbers 728/30, 512/418 is
GCF of Numerators i.e. for 728,512 is 8
LCM of denominators i.e. for 30,418 is 6270.
Thus, GCF of Fractions is 8/6270.Finally, GCF of Fractions for 728/30, 512/418 is 8/6270.