GCF of 512/726, 107/400
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 512/726, 107/400 i.e 1/145200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 512/726, 107/400.
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 512/726,107/400?
Given fractions are 512/726,107/400
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 512/726,107/400, numerators are 512,107
Denominators are 726,400
The GCF of 512,107 is 1 .
LCM of 726,400 is 145200.
The greatest common factor of 512/726,107/400 = [GCF of 512,107]/[LCM of 726,400]= 1/145200
Therefore, the GCF of 512/726,107/400 is 1/145200.
To find the highest common factor of 512,107, we have to find the factors of both numbers and list the highest common factor.
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The factors of 107 are 1, 107
The HCF of 512,107 is 1.
Lets's calculate GCF of 512,107
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 512,107 By Matching Biggest Common Factor Method
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Now, list down the factors of 107
:1,107
Greatest Common Factor
We found the factors 512,107 . The biggest common factor number is the GCF number.
So the greatest common factor 512,107 is 1.
Lets's calculate LCM of 726,400
| 2 | 726, 400 |
| 363, 200 |
∴ So the LCM of the given numbers is 2 x 363 x 200 = 145200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/145200
Therefore, the GCF of Fractions 512/726,107/400 is 1/145200
Least Common Multiple of 726,400 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 726,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(726,400) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(726,400) x common factors =2 x 1 = 2
LCM(726,400) = ( 726 × 400 ) / 2
LCM(726,400) = 290400 / 2
LCM(726,400) = 145200
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FAQs on GCF of Fractions of 512/726, 107/400
1. What is the HCF of 512,107?
The HCF of 512,107 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 512/726, 107/400?
Answer: GCF of Numerators as per given numbers 512/726, 107/400 is
GCF of Numerators i.e. for 512,107 is 1
LCM of denominators i.e. for 726,400 is 145200.
Thus, GCF of Fractions is 1/145200.Finally, GCF of Fractions for 512/726, 107/400 is 1/145200.