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GCF of 8064/443, 9600/308

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 8064/443, 9600/308 i.e 384/136444 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8064/443, 9600/308.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 8064/443,9600/308?

Given fractions are 8064/443,9600/308

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 8064/443,9600/308, numerators are 8064,9600

Denominators are 443,308

The GCF of 8064,9600 is 384 .

LCM of 443,308 is 136444.

The greatest common factor of 8064/443,9600/308 = [GCF of 8064,9600]/[LCM of 443,308]= 384/136444

Therefore, the GCF of 8064/443,9600/308 is 384/136444.

Greatest Common Factor of 8064,9600

To find the highest common factor of 8064,9600, we have to find the factors of both numbers and list the highest common factor.

The factors of 8064 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 288, 336, 384, 448, 504, 576, 672, 896, 1008, 1152, 1344, 2016, 2688, 4032, 8064

The factors of 9600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600

The HCF of 8064,9600 is 384.

Lets's calculate GCF of 8064,9600

Greatest Common Factor (GCF) of 8064,9600 By Common Division

2 8064, 9600
2 4032, 4800
2 2016, 2400
2 1008, 1200
2 504, 600
2 252, 300
2 126, 150
3 63, 75
21, 25

∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 384

Greatest Common Factor of 8064,9600 By Matching Biggest Common Factor Method

Greatest Common Factor of 8064,9600 By Matching Biggest Common Factor Method

Now, list down the factors of 8064

:

1,2,3,4,6,7,8,9,12,14,16,18,21,24,28,32,36,42,48,56,63,64,72,84,96,112,126,128,144,168,192,224,252,288,336,384,448,504,576,672,896,1008,1152,1344,2016,2688,4032,8064

Now, list down the factors of 9600

:

1,2,3,4,5,6,8,10,12,15,16,20,24,25,30,32,40,48,50,60,64,75,80,96,100,120,128,150,160,192,200,240,300,320,384,400,480,600,640,800,960,1200,1600,1920,2400,3200,4800,9600

Greatest Common Factor

We found the factors 8064,9600 . The biggest common factor number is the GCF number.
So the greatest common factor 8064,9600 is 384.

Lets's calculate LCM of 443,308

Lowest Common Multiple of 443,308 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 136444

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 384/136444

Therefore, the GCF of Fractions 8064/443,9600/308 is 384/136444

Least Common Multiple of 443,308 with GCF Formula

Least Common Multiple of 443,308 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 443,308 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(443,308) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(443,308) x common factors =1 x 1 = 1

LCM(443,308) = ( 443 × 308 ) / 1

LCM(443,308) = 136444 / 1

LCM(443,308) = 136444


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FAQs on GCF of Fractions of 8064/443, 9600/308

1. What is the HCF of 8064,9600?

The HCF of 8064,9600 is 384

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 8064/443, 9600/308?

Answer: GCF of Numerators as per given numbers 8064/443, 9600/308 is

GCF of Numerators i.e. for 8064,9600 is 384

LCM of denominators i.e. for 443,308 is 136444.

Thus, GCF of Fractions is 384/136444.Finally, GCF of Fractions for 8064/443, 9600/308 is 384/136444.