GCF of 512/568, 1338/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 512/568, 1338/414 i.e 2/117576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 512/568, 1338/414.
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 512/568,1338/414?
Given fractions are 512/568,1338/414
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 512/568,1338/414, numerators are 512,1338
Denominators are 568,414
The GCF of 512,1338 is 2 .
LCM of 568,414 is 117576.
The greatest common factor of 512/568,1338/414 = [GCF of 512,1338]/[LCM of 568,414]= 2/117576
Therefore, the GCF of 512/568,1338/414 is 2/117576.
To find the highest common factor of 512,1338, 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 1338 are 1, 2, 3, 6, 223, 446, 669, 1338
The HCF of 512,1338 is 2.
Lets's calculate GCF of 512,1338
| 2 | 512, 1338 |
| 256, 669 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 512,1338 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 1338
:1,2,3,6,223,446,669,1338
Greatest Common Factor
We found the factors 512,1338 . The biggest common factor number is the GCF number.
So the greatest common factor 512,1338 is 2.
Lets's calculate LCM of 568,414
| 2 | 568, 414 |
| 284, 207 |
∴ So the LCM of the given numbers is 2 x 284 x 207 = 117576
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/117576
Therefore, the GCF of Fractions 512/568,1338/414 is 2/117576
Least Common Multiple of 568,414 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 568,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(568,414) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(568,414) x common factors =2 x 1 = 2
LCM(568,414) = ( 568 × 414 ) / 2
LCM(568,414) = 235152 / 2
LCM(568,414) = 117576
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FAQs on GCF of Fractions of 512/568, 1338/414
1. What is the HCF of 512,1338?
The HCF of 512,1338 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 512/568, 1338/414?
Answer: GCF of Numerators as per given numbers 512/568, 1338/414 is
GCF of Numerators i.e. for 512,1338 is 2
LCM of denominators i.e. for 568,414 is 117576.
Thus, GCF of Fractions is 2/117576.Finally, GCF of Fractions for 512/568, 1338/414 is 2/117576.