GCF of 8505/415, 8070/985
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8505/415, 8070/985 i.e 15/81755 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8505/415, 8070/985.
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 8505/415,8070/985?
Given fractions are 8505/415,8070/985
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 8505/415,8070/985, numerators are 8505,8070
Denominators are 415,985
The GCF of 8505,8070 is 15 .
LCM of 415,985 is 81755.
The greatest common factor of 8505/415,8070/985 = [GCF of 8505,8070]/[LCM of 415,985]= 15/81755
Therefore, the GCF of 8505/415,8070/985 is 15/81755.
To find the highest common factor of 8505,8070, we have to find the factors of both numbers and list the highest common factor.
The factors of 8505 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 81, 105, 135, 189, 243, 315, 405, 567, 945, 1215, 1701, 2835, 8505
The factors of 8070 are 1, 2, 3, 5, 6, 10, 15, 30, 269, 538, 807, 1345, 1614, 2690, 4035, 8070
The HCF of 8505,8070 is 15.
Lets's calculate GCF of 8505,8070
| 3 | 8505, 8070 |
| 5 | 2835, 2690 |
| 567, 538 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 8505,8070 By Matching Biggest Common Factor Method
Now, list down the factors of 8505
:1,3,5,7,9,15,21,27,35,45,63,81,105,135,189,243,315,405,567,945,1215,1701,2835,8505
Now, list down the factors of 8070
:1,2,3,5,6,10,15,30,269,538,807,1345,1614,2690,4035,8070
Greatest Common Factor
We found the factors 8505,8070 . The biggest common factor number is the GCF number.
So the greatest common factor 8505,8070 is 15.
Lets's calculate LCM of 415,985
| 5 | 415, 985 |
| 83, 197 |
∴ So the LCM of the given numbers is 5 x 83 x 197 = 81755
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/81755
Therefore, the GCF of Fractions 8505/415,8070/985 is 15/81755
Least Common Multiple of 415,985 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 415,985 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(415,985) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(415,985) x common factors =5 x 1 = 5
LCM(415,985) = ( 415 × 985 ) / 5
LCM(415,985) = 408775 / 5
LCM(415,985) = 81755
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FAQs on GCF of Fractions of 8505/415, 8070/985
1. What is the HCF of 8505,8070?
The HCF of 8505,8070 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 8505/415, 8070/985?
Answer: GCF of Numerators as per given numbers 8505/415, 8070/985 is
GCF of Numerators i.e. for 8505,8070 is 15
LCM of denominators i.e. for 415,985 is 81755.
Thus, GCF of Fractions is 15/81755.Finally, GCF of Fractions for 8505/415, 8070/985 is 15/81755.