GCF of 285/40, 690/205
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 285/40, 690/205 i.e 15/1640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 285/40, 690/205.
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 285/40,690/205?
Given fractions are 285/40,690/205
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 285/40,690/205, numerators are 285,690
Denominators are 40,205
The GCF of 285,690 is 15 .
LCM of 40,205 is 1640.
The greatest common factor of 285/40,690/205 = [GCF of 285,690]/[LCM of 40,205]= 15/1640
Therefore, the GCF of 285/40,690/205 is 15/1640.
To find the highest common factor of 285,690, 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 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
The HCF of 285,690 is 15.
Lets's calculate GCF of 285,690
| 3 | 285, 690 |
| 5 | 95, 230 |
| 19, 46 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 285,690 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 690
:1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690
Greatest Common Factor
We found the factors 285,690 . The biggest common factor number is the GCF number.
So the greatest common factor 285,690 is 15.
Lets's calculate LCM of 40,205
| 5 | 40, 205 |
| 8, 41 |
∴ So the LCM of the given numbers is 5 x 8 x 41 = 1640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/1640
Therefore, the GCF of Fractions 285/40,690/205 is 15/1640
Least Common Multiple of 40,205 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 40,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,205) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(40,205) x common factors =5 x 1 = 5
LCM(40,205) = ( 40 × 205 ) / 5
LCM(40,205) = 8200 / 5
LCM(40,205) = 1640
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FAQs on GCF of Fractions of 285/40, 690/205
1. What is the HCF of 285,690?
The HCF of 285,690 is 15
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 285/40, 690/205?
Answer: GCF of Numerators as per given numbers 285/40, 690/205 is
GCF of Numerators i.e. for 285,690 is 15
LCM of denominators i.e. for 40,205 is 1640.
Thus, GCF of Fractions is 15/1640.Finally, GCF of Fractions for 285/40, 690/205 is 15/1640.