GCF of 114/772, 6000/8973
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 114/772, 6000/8973 i.e 6/6927156 easily. The following is the detailed procedure to determine the greatest common factor of fractions 114/772, 6000/8973.
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 114/772,6000/8973?
Given fractions are 114/772,6000/8973
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 114/772,6000/8973, numerators are 114,6000
Denominators are 772,8973
The GCF of 114,6000 is 6 .
LCM of 772,8973 is 6927156.
The greatest common factor of 114/772,6000/8973 = [GCF of 114,6000]/[LCM of 772,8973]= 6/6927156
Therefore, the GCF of 114/772,6000/8973 is 6/6927156.
To find the highest common factor of 114,6000, we have to find the factors of both numbers and list the highest common factor.
The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114
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 114,6000 is 6.
Lets's calculate GCF of 114,6000
| 2 | 114, 6000 |
| 3 | 57, 3000 |
| 19, 1000 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 114,6000 By Matching Biggest Common Factor Method
Now, list down the factors of 114
:1,2,3,6,19,38,57,114
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 114,6000 . The biggest common factor number is the GCF number.
So the greatest common factor 114,6000 is 6.
Lets's calculate LCM of 772,8973
Given numbers has no common factors except 1. So, there LCM is their product i.e 6927156
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/6927156
Therefore, the GCF of Fractions 114/772,6000/8973 is 6/6927156
Least Common Multiple of 772,8973 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 772,8973 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(772,8973) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(772,8973) x common factors =1 x 1 = 1
LCM(772,8973) = ( 772 × 8973 ) / 1
LCM(772,8973) = 6927156 / 1
LCM(772,8973) = 6927156
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FAQs on GCF of Fractions of 114/772, 6000/8973
1. What is the HCF of 114,6000?
The HCF of 114,6000 is 6
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 114/772, 6000/8973?
Answer: GCF of Numerators as per given numbers 114/772, 6000/8973 is
GCF of Numerators i.e. for 114,6000 is 6
LCM of denominators i.e. for 772,8973 is 6927156.
Thus, GCF of Fractions is 6/6927156.Finally, GCF of Fractions for 114/772, 6000/8973 is 6/6927156.