GCF of 288/576, 384/201
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 288/576, 384/201 i.e 96/38592 easily. The following is the detailed procedure to determine the greatest common factor of fractions 288/576, 384/201.
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 288/576,384/201?
Given fractions are 288/576,384/201
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 288/576,384/201, numerators are 288,384
Denominators are 576,201
The GCF of 288,384 is 96 .
LCM of 576,201 is 38592.
The greatest common factor of 288/576,384/201 = [GCF of 288,384]/[LCM of 576,201]= 96/38592
Therefore, the GCF of 288/576,384/201 is 96/38592.
To find the highest common factor of 288,384, we have to find the factors of both numbers and list the highest common factor.
The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The HCF of 288,384 is 96.
Lets's calculate GCF of 288,384
| 2 | 288, 384 |
| 2 | 144, 192 |
| 2 | 72, 96 |
| 2 | 36, 48 |
| 2 | 18, 24 |
| 3 | 9, 12 |
| 3, 4 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 = 96
Greatest Common Factor of 288,384 By Matching Biggest Common Factor Method
Now, list down the factors of 288
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Greatest Common Factor
We found the factors 288,384 . The biggest common factor number is the GCF number.
So the greatest common factor 288,384 is 96.
Lets's calculate LCM of 576,201
| 3 | 576, 201 |
| 192, 67 |
∴ So the LCM of the given numbers is 3 x 192 x 67 = 38592
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 96/38592
Therefore, the GCF of Fractions 288/576,384/201 is 96/38592
Least Common Multiple of 576,201 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 576,201 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(576,201) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(576,201) x common factors =3 x 1 = 3
LCM(576,201) = ( 576 × 201 ) / 3
LCM(576,201) = 115776 / 3
LCM(576,201) = 38592
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FAQs on GCF of Fractions of 288/576, 384/201
1. What is the HCF of 288,384?
The HCF of 288,384 is 96
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 288/576, 384/201?
Answer: GCF of Numerators as per given numbers 288/576, 384/201 is
GCF of Numerators i.e. for 288,384 is 96
LCM of denominators i.e. for 576,201 is 38592.
Thus, GCF of Fractions is 96/38592.Finally, GCF of Fractions for 288/576, 384/201 is 96/38592.