GCF of 417/866, 2109/208
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 417/866, 2109/208 i.e 3/90064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 417/866, 2109/208.
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 417/866,2109/208?
Given fractions are 417/866,2109/208
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 417/866,2109/208, numerators are 417,2109
Denominators are 866,208
The GCF of 417,2109 is 3 .
LCM of 866,208 is 90064.
The greatest common factor of 417/866,2109/208 = [GCF of 417,2109]/[LCM of 866,208]= 3/90064
Therefore, the GCF of 417/866,2109/208 is 3/90064.
To find the highest common factor of 417,2109, we have to find the factors of both numbers and list the highest common factor.
The factors of 417 are 1, 3, 139, 417
The factors of 2109 are 1, 3, 19, 37, 57, 111, 703, 2109
The HCF of 417,2109 is 3.
Lets's calculate GCF of 417,2109
| 3 | 417, 2109 |
| 139, 703 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 417,2109 By Matching Biggest Common Factor Method
Now, list down the factors of 417
:1,3,139,417
Now, list down the factors of 2109
:1,3,19,37,57,111,703,2109
Greatest Common Factor
We found the factors 417,2109 . The biggest common factor number is the GCF number.
So the greatest common factor 417,2109 is 3.
Lets's calculate LCM of 866,208
| 2 | 866, 208 |
| 433, 104 |
∴ So the LCM of the given numbers is 2 x 433 x 104 = 90064
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/90064
Therefore, the GCF of Fractions 417/866,2109/208 is 3/90064
Least Common Multiple of 866,208 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 866,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(866,208) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(866,208) x common factors =2 x 1 = 2
LCM(866,208) = ( 866 × 208 ) / 2
LCM(866,208) = 180128 / 2
LCM(866,208) = 90064
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FAQs on GCF of Fractions of 417/866, 2109/208
1. What is the HCF of 417,2109?
The HCF of 417,2109 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 417/866, 2109/208?
Answer: GCF of Numerators as per given numbers 417/866, 2109/208 is
GCF of Numerators i.e. for 417,2109 is 3
LCM of denominators i.e. for 866,208 is 90064.
Thus, GCF of Fractions is 3/90064.Finally, GCF of Fractions for 417/866, 2109/208 is 3/90064.