GCF of 285/499, 309/461
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 285/499, 309/461 i.e 3/230039 easily. The following is the detailed procedure to determine the greatest common factor of fractions 285/499, 309/461.
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 285/499,309/461?
Given fractions are 285/499,309/461
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 285/499,309/461, numerators are 285,309
Denominators are 499,461
The GCF of 285,309 is 3 .
LCM of 499,461 is 230039.
The greatest common factor of 285/499,309/461 = [GCF of 285,309]/[LCM of 499,461]= 3/230039
Therefore, the GCF of 285/499,309/461 is 3/230039.
To find the highest common factor of 285,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 285 are 1, 3, 5, 15, 19, 57, 95, 285
The factors of 309 are 1, 3, 103, 309
The HCF of 285,309 is 3.
Lets's calculate GCF of 285,309
| 3 | 285, 309 |
| 95, 103 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 285,309 By Matching Biggest Common Factor Method
Now, list down the factors of 285
:1,3,5,15,19,57,95,285
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 285,309 . The biggest common factor number is the GCF number.
So the greatest common factor 285,309 is 3.
Lets's calculate LCM of 499,461
Given numbers has no common factors except 1. So, there LCM is their product i.e 230039
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/230039
Therefore, the GCF of Fractions 285/499,309/461 is 3/230039
Least Common Multiple of 499,461 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 499,461 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(499,461) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(499,461) x common factors =1 x 1 = 1
LCM(499,461) = ( 499 × 461 ) / 1
LCM(499,461) = 230039 / 1
LCM(499,461) = 230039
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FAQs on GCF of Fractions of 285/499, 309/461
1. What is the HCF of 285,309?
The HCF of 285,309 is 3
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 285/499, 309/461?
Answer: GCF of Numerators as per given numbers 285/499, 309/461 is
GCF of Numerators i.e. for 285,309 is 3
LCM of denominators i.e. for 499,461 is 230039.
Thus, GCF of Fractions is 3/230039.Finally, GCF of Fractions for 285/499, 309/461 is 3/230039.