GCF of 3712/227, 8000/9208
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3712/227, 8000/9208 i.e 64/2090216 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3712/227, 8000/9208.
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 3712/227,8000/9208?
Given fractions are 3712/227,8000/9208
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 3712/227,8000/9208, numerators are 3712,8000
Denominators are 227,9208
The GCF of 3712,8000 is 64 .
LCM of 227,9208 is 2090216.
The greatest common factor of 3712/227,8000/9208 = [GCF of 3712,8000]/[LCM of 227,9208]= 64/2090216
Therefore, the GCF of 3712/227,8000/9208 is 64/2090216.
To find the highest common factor of 3712,8000, we have to find the factors of both numbers and list the highest common factor.
The factors of 3712 are 1, 2, 4, 8, 16, 29, 32, 58, 64, 116, 128, 232, 464, 928, 1856, 3712
The factors of 8000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 800, 1000, 1600, 2000, 4000, 8000
The HCF of 3712,8000 is 64.
Lets's calculate GCF of 3712,8000
| 2 | 3712, 8000 |
| 2 | 1856, 4000 |
| 2 | 928, 2000 |
| 2 | 464, 1000 |
| 2 | 232, 500 |
| 2 | 116, 250 |
| 58, 125 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 = 64
Greatest Common Factor of 3712,8000 By Matching Biggest Common Factor Method
Now, list down the factors of 3712
:1,2,4,8,16,29,32,58,64,116,128,232,464,928,1856,3712
Now, list down the factors of 8000
:1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,125,160,200,250,320,400,500,800,1000,1600,2000,4000,8000
Greatest Common Factor
We found the factors 3712,8000 . The biggest common factor number is the GCF number.
So the greatest common factor 3712,8000 is 64.
Lets's calculate LCM of 227,9208
Given numbers has no common factors except 1. So, there LCM is their product i.e 2090216
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 64/2090216
Therefore, the GCF of Fractions 3712/227,8000/9208 is 64/2090216
Least Common Multiple of 227,9208 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 227,9208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(227,9208) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(227,9208) x common factors =1 x 1 = 1
LCM(227,9208) = ( 227 × 9208 ) / 1
LCM(227,9208) = 2090216 / 1
LCM(227,9208) = 2090216
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FAQs on GCF of Fractions of 3712/227, 8000/9208
1. What is the HCF of 3712,8000?
The HCF of 3712,8000 is 64
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 3712/227, 8000/9208?
Answer: GCF of Numerators as per given numbers 3712/227, 8000/9208 is
GCF of Numerators i.e. for 3712,8000 is 64
LCM of denominators i.e. for 227,9208 is 2090216.
Thus, GCF of Fractions is 64/2090216.Finally, GCF of Fractions for 3712/227, 8000/9208 is 64/2090216.