GCF of 384/75, 400/684
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 384/75, 400/684 i.e 16/17100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 384/75, 400/684.
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 384/75,400/684?
Given fractions are 384/75,400/684
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 384/75,400/684, numerators are 384,400
Denominators are 75,684
The GCF of 384,400 is 16 .
LCM of 75,684 is 17100.
The greatest common factor of 384/75,400/684 = [GCF of 384,400]/[LCM of 75,684]= 16/17100
Therefore, the GCF of 384/75,400/684 is 16/17100.
To find the highest common factor of 384,400, we have to find the factors of both numbers and list the highest common factor.
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The HCF of 384,400 is 16.
Lets's calculate GCF of 384,400
| 2 | 384, 400 |
| 2 | 192, 200 |
| 2 | 96, 100 |
| 2 | 48, 50 |
| 24, 25 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 384,400 By Matching Biggest Common Factor Method
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 384,400 . The biggest common factor number is the GCF number.
So the greatest common factor 384,400 is 16.
Lets's calculate LCM of 75,684
| 3 | 75, 684 |
| 25, 228 |
∴ So the LCM of the given numbers is 3 x 25 x 228 = 17100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/17100
Therefore, the GCF of Fractions 384/75,400/684 is 16/17100
Least Common Multiple of 75,684 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 75,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,684) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(75,684) x common factors =3 x 1 = 3
LCM(75,684) = ( 75 × 684 ) / 3
LCM(75,684) = 51300 / 3
LCM(75,684) = 17100
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FAQs on GCF of Fractions of 384/75, 400/684
1. What is the HCF of 384,400?
The HCF of 384,400 is 16
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 384/75, 400/684?
Answer: GCF of Numerators as per given numbers 384/75, 400/684 is
GCF of Numerators i.e. for 384,400 is 16
LCM of denominators i.e. for 75,684 is 17100.
Thus, GCF of Fractions is 16/17100.Finally, GCF of Fractions for 384/75, 400/684 is 16/17100.