GCF of 3004/814, 6000/459
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3004/814, 6000/459 i.e 4/373626 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3004/814, 6000/459.
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 3004/814,6000/459?
Given fractions are 3004/814,6000/459
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 3004/814,6000/459, numerators are 3004,6000
Denominators are 814,459
The GCF of 3004,6000 is 4 .
LCM of 814,459 is 373626.
The greatest common factor of 3004/814,6000/459 = [GCF of 3004,6000]/[LCM of 814,459]= 4/373626
Therefore, the GCF of 3004/814,6000/459 is 4/373626.
To find the highest common factor of 3004,6000, we have to find the factors of both numbers and list the highest common factor.
The factors of 3004 are 1, 2, 4, 751, 1502, 3004
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 3004,6000 is 4.
Lets's calculate GCF of 3004,6000
| 2 | 3004, 6000 |
| 2 | 1502, 3000 |
| 751, 1500 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 3004,6000 By Matching Biggest Common Factor Method
Now, list down the factors of 3004
:1,2,4,751,1502,3004
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 3004,6000 . The biggest common factor number is the GCF number.
So the greatest common factor 3004,6000 is 4.
Lets's calculate LCM of 814,459
Given numbers has no common factors except 1. So, there LCM is their product i.e 373626
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/373626
Therefore, the GCF of Fractions 3004/814,6000/459 is 4/373626
Least Common Multiple of 814,459 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 814,459 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(814,459) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(814,459) x common factors =1 x 1 = 1
LCM(814,459) = ( 814 × 459 ) / 1
LCM(814,459) = 373626 / 1
LCM(814,459) = 373626
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FAQs on GCF of Fractions of 3004/814, 6000/459
1. What is the HCF of 3004,6000?
The HCF of 3004,6000 is 4
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 3004/814, 6000/459?
Answer: GCF of Numerators as per given numbers 3004/814, 6000/459 is
GCF of Numerators i.e. for 3004,6000 is 4
LCM of denominators i.e. for 814,459 is 373626.
Thus, GCF of Fractions is 4/373626.Finally, GCF of Fractions for 3004/814, 6000/459 is 4/373626.