GCF of 338/256, 7774/384
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 338/256, 7774/384 i.e 338/768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 338/256, 7774/384.
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 338/256,7774/384?
Given fractions are 338/256,7774/384
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 338/256,7774/384, numerators are 338,7774
Denominators are 256,384
The GCF of 338,7774 is 338 .
LCM of 256,384 is 768.
The greatest common factor of 338/256,7774/384 = [GCF of 338,7774]/[LCM of 256,384]= 338/768
Therefore, the GCF of 338/256,7774/384 is 338/768.
To find the highest common factor of 338,7774, we have to find the factors of both numbers and list the highest common factor.
The factors of 338 are 1, 2, 13, 26, 169, 338
The factors of 7774 are 1, 2, 13, 23, 26, 46, 169, 299, 338, 598, 3887, 7774
The HCF of 338,7774 is 338.
Lets's calculate GCF of 338,7774
| 2 | 338, 7774 |
| 13 | 169, 3887 |
| 13 | 13, 299 |
| 1, 23 |
∴ So the GCF of the given numbers is 2 x 13 x 13 = 338
Greatest Common Factor of 338,7774 By Matching Biggest Common Factor Method
Now, list down the factors of 338
:1,2,13,26,169,338
Now, list down the factors of 7774
:1,2,13,23,26,46,169,299,338,598,3887,7774
Greatest Common Factor
We found the factors 338,7774 . The biggest common factor number is the GCF number.
So the greatest common factor 338,7774 is 338.
Lets's calculate LCM of 256,384
| 2 | 256, 384 |
| 2 | 128, 192 |
| 2 | 64, 96 |
| 2 | 32, 48 |
| 2 | 16, 24 |
| 2 | 8, 12 |
| 2 | 4, 6 |
| 2, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 768
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 338/768
Therefore, the GCF of Fractions 338/256,7774/384 is 338/768
Least Common Multiple of 256,384 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 256,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(256,384) = 128
common factors(in case of two or more numbers have common factors) = 1
GCF(256,384) x common factors =128 x 1 = 128
LCM(256,384) = ( 256 × 384 ) / 128
LCM(256,384) = 98304 / 128
LCM(256,384) = 768
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FAQs on GCF of Fractions of 338/256, 7774/384
1. What is the HCF of 338,7774?
The HCF of 338,7774 is 338
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 338/256, 7774/384?
Answer: GCF of Numerators as per given numbers 338/256, 7774/384 is
GCF of Numerators i.e. for 338,7774 is 338
LCM of denominators i.e. for 256,384 is 768.
Thus, GCF of Fractions is 338/768.Finally, GCF of Fractions for 338/256, 7774/384 is 338/768.