GCF of 2967/258, 6000/1784
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2967/258, 6000/1784 i.e 3/230136 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2967/258, 6000/1784.
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 2967/258,6000/1784?
Given fractions are 2967/258,6000/1784
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 2967/258,6000/1784, numerators are 2967,6000
Denominators are 258,1784
The GCF of 2967,6000 is 3 .
LCM of 258,1784 is 230136.
The greatest common factor of 2967/258,6000/1784 = [GCF of 2967,6000]/[LCM of 258,1784]= 3/230136
Therefore, the GCF of 2967/258,6000/1784 is 3/230136.
To find the highest common factor of 2967,6000, we have to find the factors of both numbers and list the highest common factor.
The factors of 2967 are 1, 3, 23, 43, 69, 129, 989, 2967
The factors of 6000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000, 6000
The HCF of 2967,6000 is 3.
Lets's calculate GCF of 2967,6000
| 3 | 2967, 6000 |
| 989, 2000 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2967,6000 By Matching Biggest Common Factor Method
Now, list down the factors of 2967
:1,3,23,43,69,129,989,2967
Now, list down the factors of 6000
:1,2,3,4,5,6,8,10,12,15,16,20,24,25,30,40,48,50,60,75,80,100,120,125,150,200,240,250,300,375,400,500,600,750,1000,1200,1500,2000,3000,6000
Greatest Common Factor
We found the factors 2967,6000 . The biggest common factor number is the GCF number.
So the greatest common factor 2967,6000 is 3.
Lets's calculate LCM of 258,1784
| 2 | 258, 1784 |
| 129, 892 |
∴ So the LCM of the given numbers is 2 x 129 x 892 = 230136
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/230136
Therefore, the GCF of Fractions 2967/258,6000/1784 is 3/230136
Least Common Multiple of 258,1784 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 258,1784 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(258,1784) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(258,1784) x common factors =2 x 1 = 2
LCM(258,1784) = ( 258 × 1784 ) / 2
LCM(258,1784) = 460272 / 2
LCM(258,1784) = 230136
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FAQs on GCF of Fractions of 2967/258, 6000/1784
1. What is the HCF of 2967,6000?
The HCF of 2967,6000 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 2967/258, 6000/1784?
Answer: GCF of Numerators as per given numbers 2967/258, 6000/1784 is
GCF of Numerators i.e. for 2967,6000 is 3
LCM of denominators i.e. for 258,1784 is 230136.
Thus, GCF of Fractions is 3/230136.Finally, GCF of Fractions for 2967/258, 6000/1784 is 3/230136.