GCF of 285/86, 165/40, 406/64
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 285/86, 165/40, 406/64 i.e 1/13760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 285/86, 165/40, 406/64.
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 285/86,165/40,406/64?
Given fractions are 285/86,165/40,406/64
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 285/86,165/40,406/64, numerators are 285,165,406
Denominators are 86,40,64
The GCF of 285,165,406 is 1 .
LCM of 86,40,64 is 13760.
The greatest common factor of 285/86,165/40,406/64 = [GCF of 285,165,406]/[LCM of 86,40,64]= 1/13760
Therefore, the GCF of 285/86,165/40,406/64 is 1/13760.
To find the highest common factor of 285,165,406, 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 165 are 1, 3, 5, 11, 15, 33, 55, 165
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 285,165,406 is 1.
Lets's calculate GCF of 285,165,406
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 285,165,406 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 165
:1,3,5,11,15,33,55,165
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 285,165,406 . The biggest common factor number is the GCF number.
So the greatest common factor 285,165,406 is 1.
Lets's calculate LCM of 86,40,64
| 2 | 86, 40, 64 |
| 2 | 43, 20, 32 |
| 2 | 43, 10, 16 |
| 43, 5, 8 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 43 x 5 x 8 = 13760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13760
Therefore, the GCF of Fractions 285/86,165/40,406/64 is 1/13760
Least Common Multiple of 86,40,64 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 86,40,64 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(86,40,64) = 2
common factors(in case of two or more numbers have common factors) = 8
GCF(86,40,64) x common factors =2 x 8 = 16
LCM(86,40,64) = ( 86 × 40 × 64 ) / 16
LCM(86,40,64) = 220160 / 16
LCM(86,40,64) = 13760
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FAQs on GCF of Fractions of 285/86, 165/40, 406/64
1. What is the HCF of 285,165,406?
The HCF of 285,165,406 is 1
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 285/86, 165/40, 406/64?
Answer: GCF of Numerators as per given numbers 285/86, 165/40, 406/64 is
GCF of Numerators i.e. for 285,165,406 is 1
LCM of denominators i.e. for 86,40,64 is 13760.
Thus, GCF of Fractions is 1/13760.Finally, GCF of Fractions for 285/86, 165/40, 406/64 is 1/13760.