GCF of 2769/669, 9600/7314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2769/669, 9600/7314 i.e 3/1631022 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2769/669, 9600/7314.
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 2769/669,9600/7314?
Given fractions are 2769/669,9600/7314
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 2769/669,9600/7314, numerators are 2769,9600
Denominators are 669,7314
The GCF of 2769,9600 is 3 .
LCM of 669,7314 is 1631022.
The greatest common factor of 2769/669,9600/7314 = [GCF of 2769,9600]/[LCM of 669,7314]= 3/1631022
Therefore, the GCF of 2769/669,9600/7314 is 3/1631022.
To find the highest common factor of 2769,9600, we have to find the factors of both numbers and list the highest common factor.
The factors of 2769 are 1, 3, 13, 39, 71, 213, 923, 2769
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 2769,9600 is 3.
Lets's calculate GCF of 2769,9600
| 3 | 2769, 9600 |
| 923, 3200 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2769,9600 By Matching Biggest Common Factor Method
Now, list down the factors of 2769
:1,3,13,39,71,213,923,2769
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 2769,9600 . The biggest common factor number is the GCF number.
So the greatest common factor 2769,9600 is 3.
Lets's calculate LCM of 669,7314
| 3 | 669, 7314 |
| 223, 2438 |
∴ So the LCM of the given numbers is 3 x 223 x 2438 = 1631022
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1631022
Therefore, the GCF of Fractions 2769/669,9600/7314 is 3/1631022
Least Common Multiple of 669,7314 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 669,7314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(669,7314) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(669,7314) x common factors =3 x 1 = 3
LCM(669,7314) = ( 669 × 7314 ) / 3
LCM(669,7314) = 4893066 / 3
LCM(669,7314) = 1631022
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FAQs on GCF of Fractions of 2769/669, 9600/7314
1. What is the HCF of 2769,9600?
The HCF of 2769,9600 is 3
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 2769/669, 9600/7314?
Answer: GCF of Numerators as per given numbers 2769/669, 9600/7314 is
GCF of Numerators i.e. for 2769,9600 is 3
LCM of denominators i.e. for 669,7314 is 1631022.
Thus, GCF of Fractions is 3/1631022.Finally, GCF of Fractions for 2769/669, 9600/7314 is 3/1631022.