GCF of 6000/523, 8376/4140
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6000/523, 8376/4140 i.e 24/2165220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6000/523, 8376/4140.
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 6000/523,8376/4140?
Given fractions are 6000/523,8376/4140
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 6000/523,8376/4140, numerators are 6000,8376
Denominators are 523,4140
The GCF of 6000,8376 is 24 .
LCM of 523,4140 is 2165220.
The greatest common factor of 6000/523,8376/4140 = [GCF of 6000,8376]/[LCM of 523,4140]= 24/2165220
Therefore, the GCF of 6000/523,8376/4140 is 24/2165220.
To find the highest common factor of 6000,8376, we have to find the factors of both numbers and list the highest common factor.
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 factors of 8376 are 1, 2, 3, 4, 6, 8, 12, 24, 349, 698, 1047, 1396, 2094, 2792, 4188, 8376
The HCF of 6000,8376 is 24.
Lets's calculate GCF of 6000,8376
| 2 | 6000, 8376 |
| 2 | 3000, 4188 |
| 2 | 1500, 2094 |
| 3 | 750, 1047 |
| 250, 349 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 6000,8376 By Matching Biggest Common Factor Method
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
Now, list down the factors of 8376
:1,2,3,4,6,8,12,24,349,698,1047,1396,2094,2792,4188,8376
Greatest Common Factor
We found the factors 6000,8376 . The biggest common factor number is the GCF number.
So the greatest common factor 6000,8376 is 24.
Lets's calculate LCM of 523,4140
Given numbers has no common factors except 1. So, there LCM is their product i.e 2165220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/2165220
Therefore, the GCF of Fractions 6000/523,8376/4140 is 24/2165220
Least Common Multiple of 523,4140 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 523,4140 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(523,4140) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(523,4140) x common factors =1 x 1 = 1
LCM(523,4140) = ( 523 × 4140 ) / 1
LCM(523,4140) = 2165220 / 1
LCM(523,4140) = 2165220
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FAQs on GCF of Fractions of 6000/523, 8376/4140
1. What is the HCF of 6000,8376?
The HCF of 6000,8376 is 24
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 6000/523, 8376/4140?
Answer: GCF of Numerators as per given numbers 6000/523, 8376/4140 is
GCF of Numerators i.e. for 6000,8376 is 24
LCM of denominators i.e. for 523,4140 is 2165220.
Thus, GCF of Fractions is 24/2165220.Finally, GCF of Fractions for 6000/523, 8376/4140 is 24/2165220.