GCF of 415/31, 285/478
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 415/31, 285/478 i.e 5/14818 easily. The following is the detailed procedure to determine the greatest common factor of fractions 415/31, 285/478.
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 415/31,285/478?
Given fractions are 415/31,285/478
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 415/31,285/478, numerators are 415,285
Denominators are 31,478
The GCF of 415,285 is 5 .
LCM of 31,478 is 14818.
The greatest common factor of 415/31,285/478 = [GCF of 415,285]/[LCM of 31,478]= 5/14818
Therefore, the GCF of 415/31,285/478 is 5/14818.
To find the highest common factor of 415,285, we have to find the factors of both numbers and list the highest common factor.
The factors of 415 are 1, 5, 83, 415
The factors of 285 are 1, 3, 5, 15, 19, 57, 95, 285
The HCF of 415,285 is 5.
Lets's calculate GCF of 415,285
| 5 | 415, 285 |
| 83, 57 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 415,285 By Matching Biggest Common Factor Method
Now, list down the factors of 415
:1,5,83,415
Now, list down the factors of 285
:1,3,5,15,19,57,95,285
Greatest Common Factor
We found the factors 415,285 . The biggest common factor number is the GCF number.
So the greatest common factor 415,285 is 5.
Lets's calculate LCM of 31,478
Given numbers has no common factors except 1. So, there LCM is their product i.e 14818
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/14818
Therefore, the GCF of Fractions 415/31,285/478 is 5/14818
Least Common Multiple of 31,478 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 31,478 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,478) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,478) x common factors =1 x 1 = 1
LCM(31,478) = ( 31 × 478 ) / 1
LCM(31,478) = 14818 / 1
LCM(31,478) = 14818
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FAQs on GCF of Fractions of 415/31, 285/478
1. What is the HCF of 415,285?
The HCF of 415,285 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 415/31, 285/478?
Answer: GCF of Numerators as per given numbers 415/31, 285/478 is
GCF of Numerators i.e. for 415,285 is 5
LCM of denominators i.e. for 31,478 is 14818.
Thus, GCF of Fractions is 5/14818.Finally, GCF of Fractions for 415/31, 285/478 is 5/14818.