GCF of 8085/414, 5830/894
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8085/414, 5830/894 i.e 55/61686 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8085/414, 5830/894.
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 8085/414,5830/894?
Given fractions are 8085/414,5830/894
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 8085/414,5830/894, numerators are 8085,5830
Denominators are 414,894
The GCF of 8085,5830 is 55 .
LCM of 414,894 is 61686.
The greatest common factor of 8085/414,5830/894 = [GCF of 8085,5830]/[LCM of 414,894]= 55/61686
Therefore, the GCF of 8085/414,5830/894 is 55/61686.
To find the highest common factor of 8085,5830, we have to find the factors of both numbers and list the highest common factor.
The factors of 8085 are 1, 3, 5, 7, 11, 15, 21, 33, 35, 49, 55, 77, 105, 147, 165, 231, 245, 385, 539, 735, 1155, 1617, 2695, 8085
The factors of 5830 are 1, 2, 5, 10, 11, 22, 53, 55, 106, 110, 265, 530, 583, 1166, 2915, 5830
The HCF of 8085,5830 is 55.
Lets's calculate GCF of 8085,5830
| 5 | 8085, 5830 |
| 11 | 1617, 1166 |
| 147, 106 |
∴ So the GCF of the given numbers is 5 x 11 = 55
Greatest Common Factor of 8085,5830 By Matching Biggest Common Factor Method
Now, list down the factors of 8085
:1,3,5,7,11,15,21,33,35,49,55,77,105,147,165,231,245,385,539,735,1155,1617,2695,8085
Now, list down the factors of 5830
:1,2,5,10,11,22,53,55,106,110,265,530,583,1166,2915,5830
Greatest Common Factor
We found the factors 8085,5830 . The biggest common factor number is the GCF number.
So the greatest common factor 8085,5830 is 55.
Lets's calculate LCM of 414,894
| 2 | 414, 894 |
| 3 | 207, 447 |
| 69, 149 |
∴ So the LCM of the given numbers is 2 x 3 x 69 x 149 = 61686
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 55/61686
Therefore, the GCF of Fractions 8085/414,5830/894 is 55/61686
Least Common Multiple of 414,894 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 414,894 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,894) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(414,894) x common factors =6 x 1 = 6
LCM(414,894) = ( 414 × 894 ) / 6
LCM(414,894) = 370116 / 6
LCM(414,894) = 61686
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FAQs on GCF of Fractions of 8085/414, 5830/894
1. What is the HCF of 8085,5830?
The HCF of 8085,5830 is 55
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 8085/414, 5830/894?
Answer: GCF of Numerators as per given numbers 8085/414, 5830/894 is
GCF of Numerators i.e. for 8085,5830 is 55
LCM of denominators i.e. for 414,894 is 61686.
Thus, GCF of Fractions is 55/61686.Finally, GCF of Fractions for 8085/414, 5830/894 is 55/61686.