GCF of 4085/512, 9075/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4085/512, 9075/814 i.e 5/208384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4085/512, 9075/814.
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 4085/512,9075/814?
Given fractions are 4085/512,9075/814
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 4085/512,9075/814, numerators are 4085,9075
Denominators are 512,814
The GCF of 4085,9075 is 5 .
LCM of 512,814 is 208384.
The greatest common factor of 4085/512,9075/814 = [GCF of 4085,9075]/[LCM of 512,814]= 5/208384
Therefore, the GCF of 4085/512,9075/814 is 5/208384.
To find the highest common factor of 4085,9075, we have to find the factors of both numbers and list the highest common factor.
The factors of 4085 are 1, 5, 19, 43, 95, 215, 817, 4085
The factors of 9075 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 121, 165, 275, 363, 605, 825, 1815, 3025, 9075
The HCF of 4085,9075 is 5.
Lets's calculate GCF of 4085,9075
| 5 | 4085, 9075 |
| 817, 1815 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 4085,9075 By Matching Biggest Common Factor Method
Now, list down the factors of 4085
:1,5,19,43,95,215,817,4085
Now, list down the factors of 9075
:1,3,5,11,15,25,33,55,75,121,165,275,363,605,825,1815,3025,9075
Greatest Common Factor
We found the factors 4085,9075 . The biggest common factor number is the GCF number.
So the greatest common factor 4085,9075 is 5.
Lets's calculate LCM of 512,814
| 2 | 512, 814 |
| 256, 407 |
∴ So the LCM of the given numbers is 2 x 256 x 407 = 208384
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/208384
Therefore, the GCF of Fractions 4085/512,9075/814 is 5/208384
Least Common Multiple of 512,814 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 512,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,814) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(512,814) x common factors =2 x 1 = 2
LCM(512,814) = ( 512 × 814 ) / 2
LCM(512,814) = 416768 / 2
LCM(512,814) = 208384
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FAQs on GCF of Fractions of 4085/512, 9075/814
1. What is the HCF of 4085,9075?
The HCF of 4085,9075 is 5
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 4085/512, 9075/814?
Answer: GCF of Numerators as per given numbers 4085/512, 9075/814 is
GCF of Numerators i.e. for 4085,9075 is 5
LCM of denominators i.e. for 512,814 is 208384.
Thus, GCF of Fractions is 5/208384.Finally, GCF of Fractions for 4085/512, 9075/814 is 5/208384.