GCF of 1536/728, 9730/514
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1536/728, 9730/514 i.e 2/187096 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1536/728, 9730/514.
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 1536/728,9730/514?
Given fractions are 1536/728,9730/514
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 1536/728,9730/514, numerators are 1536,9730
Denominators are 728,514
The GCF of 1536,9730 is 2 .
LCM of 728,514 is 187096.
The greatest common factor of 1536/728,9730/514 = [GCF of 1536,9730]/[LCM of 728,514]= 2/187096
Therefore, the GCF of 1536/728,9730/514 is 2/187096.
To find the highest common factor of 1536,9730, we have to find the factors of both numbers and list the highest common factor.
The factors of 1536 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1536
The factors of 9730 are 1, 2, 5, 7, 10, 14, 35, 70, 139, 278, 695, 973, 1390, 1946, 4865, 9730
The HCF of 1536,9730 is 2.
Lets's calculate GCF of 1536,9730
| 2 | 1536, 9730 |
| 768, 4865 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1536,9730 By Matching Biggest Common Factor Method
Now, list down the factors of 1536
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,512,768,1536
Now, list down the factors of 9730
:1,2,5,7,10,14,35,70,139,278,695,973,1390,1946,4865,9730
Greatest Common Factor
We found the factors 1536,9730 . The biggest common factor number is the GCF number.
So the greatest common factor 1536,9730 is 2.
Lets's calculate LCM of 728,514
| 2 | 728, 514 |
| 364, 257 |
∴ So the LCM of the given numbers is 2 x 364 x 257 = 187096
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/187096
Therefore, the GCF of Fractions 1536/728,9730/514 is 2/187096
Least Common Multiple of 728,514 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 728,514 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(728,514) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(728,514) x common factors =2 x 1 = 2
LCM(728,514) = ( 728 × 514 ) / 2
LCM(728,514) = 374192 / 2
LCM(728,514) = 187096
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1536/728, 9730/514
1. What is the HCF of 1536,9730?
The HCF of 1536,9730 is 2
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 1536/728, 9730/514?
Answer: GCF of Numerators as per given numbers 1536/728, 9730/514 is
GCF of Numerators i.e. for 1536,9730 is 2
LCM of denominators i.e. for 728,514 is 187096.
Thus, GCF of Fractions is 2/187096.Finally, GCF of Fractions for 1536/728, 9730/514 is 2/187096.