GCF of 2085/984, 8214/2700
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2085/984, 8214/2700 i.e 3/221400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2085/984, 8214/2700.
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 2085/984,8214/2700?
Given fractions are 2085/984,8214/2700
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 2085/984,8214/2700, numerators are 2085,8214
Denominators are 984,2700
The GCF of 2085,8214 is 3 .
LCM of 984,2700 is 221400.
The greatest common factor of 2085/984,8214/2700 = [GCF of 2085,8214]/[LCM of 984,2700]= 3/221400
Therefore, the GCF of 2085/984,8214/2700 is 3/221400.
To find the highest common factor of 2085,8214, we have to find the factors of both numbers and list the highest common factor.
The factors of 2085 are 1, 3, 5, 15, 139, 417, 695, 2085
The factors of 8214 are 1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214
The HCF of 2085,8214 is 3.
Lets's calculate GCF of 2085,8214
| 3 | 2085, 8214 |
| 695, 2738 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2085,8214 By Matching Biggest Common Factor Method
Now, list down the factors of 2085
:1,3,5,15,139,417,695,2085
Now, list down the factors of 8214
:1,2,3,6,37,74,111,222,1369,2738,4107,8214
Greatest Common Factor
We found the factors 2085,8214 . The biggest common factor number is the GCF number.
So the greatest common factor 2085,8214 is 3.
Lets's calculate LCM of 984,2700
| 2 | 984, 2700 |
| 2 | 492, 1350 |
| 3 | 246, 675 |
| 82, 225 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 82 x 225 = 221400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/221400
Therefore, the GCF of Fractions 2085/984,8214/2700 is 3/221400
Least Common Multiple of 984,2700 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 984,2700 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(984,2700) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(984,2700) x common factors =12 x 1 = 12
LCM(984,2700) = ( 984 × 2700 ) / 12
LCM(984,2700) = 2656800 / 12
LCM(984,2700) = 221400
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FAQs on GCF of Fractions of 2085/984, 8214/2700
1. What is the HCF of 2085,8214?
The HCF of 2085,8214 is 3
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 2085/984, 8214/2700?
Answer: GCF of Numerators as per given numbers 2085/984, 8214/2700 is
GCF of Numerators i.e. for 2085,8214 is 3
LCM of denominators i.e. for 984,2700 is 221400.
Thus, GCF of Fractions is 3/221400.Finally, GCF of Fractions for 2085/984, 8214/2700 is 3/221400.