GCF of 724/10, 512/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 724/10, 512/728 i.e 4/3640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 724/10, 512/728.
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 724/10,512/728?
Given fractions are 724/10,512/728
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 724/10,512/728, numerators are 724,512
Denominators are 10,728
The GCF of 724,512 is 4 .
LCM of 10,728 is 3640.
The greatest common factor of 724/10,512/728 = [GCF of 724,512]/[LCM of 10,728]= 4/3640
Therefore, the GCF of 724/10,512/728 is 4/3640.
To find the highest common factor of 724,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 724 are 1, 2, 4, 181, 362, 724
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 724,512 is 4.
Lets's calculate GCF of 724,512
| 2 | 724, 512 |
| 2 | 362, 256 |
| 181, 128 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 724,512 By Matching Biggest Common Factor Method
Now, list down the factors of 724
:1,2,4,181,362,724
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 724,512 . The biggest common factor number is the GCF number.
So the greatest common factor 724,512 is 4.
Lets's calculate LCM of 10,728
| 2 | 10, 728 |
| 5, 364 |
∴ So the LCM of the given numbers is 2 x 5 x 364 = 3640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/3640
Therefore, the GCF of Fractions 724/10,512/728 is 4/3640
Least Common Multiple of 10,728 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 10,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(10,728) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(10,728) x common factors =2 x 1 = 2
LCM(10,728) = ( 10 × 728 ) / 2
LCM(10,728) = 7280 / 2
LCM(10,728) = 3640
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FAQs on GCF of Fractions of 724/10, 512/728
1. What is the HCF of 724,512?
The HCF of 724,512 is 4
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 724/10, 512/728?
Answer: GCF of Numerators as per given numbers 724/10, 512/728 is
GCF of Numerators i.e. for 724,512 is 4
LCM of denominators i.e. for 10,728 is 3640.
Thus, GCF of Fractions is 4/3640.Finally, GCF of Fractions for 724/10, 512/728 is 4/3640.