GCF of 8241/827, 5949/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8241/827, 5949/209 i.e 3/172843 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8241/827, 5949/209.
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 8241/827,5949/209?
Given fractions are 8241/827,5949/209
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 8241/827,5949/209, numerators are 8241,5949
Denominators are 827,209
The GCF of 8241,5949 is 3 .
LCM of 827,209 is 172843.
The greatest common factor of 8241/827,5949/209 = [GCF of 8241,5949]/[LCM of 827,209]= 3/172843
Therefore, the GCF of 8241/827,5949/209 is 3/172843.
To find the highest common factor of 8241,5949, we have to find the factors of both numbers and list the highest common factor.
The factors of 8241 are 1, 3, 41, 67, 123, 201, 2747, 8241
The factors of 5949 are 1, 3, 9, 661, 1983, 5949
The HCF of 8241,5949 is 3.
Lets's calculate GCF of 8241,5949
| 3 | 8241, 5949 |
| 2747, 1983 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 8241,5949 By Matching Biggest Common Factor Method
Now, list down the factors of 8241
:1,3,41,67,123,201,2747,8241
Now, list down the factors of 5949
:1,3,9,661,1983,5949
Greatest Common Factor
We found the factors 8241,5949 . The biggest common factor number is the GCF number.
So the greatest common factor 8241,5949 is 3.
Lets's calculate LCM of 827,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 172843
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/172843
Therefore, the GCF of Fractions 8241/827,5949/209 is 3/172843
Least Common Multiple of 827,209 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 827,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(827,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(827,209) x common factors =1 x 1 = 1
LCM(827,209) = ( 827 × 209 ) / 1
LCM(827,209) = 172843 / 1
LCM(827,209) = 172843
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FAQs on GCF of Fractions of 8241/827, 5949/209
1. What is the HCF of 8241,5949?
The HCF of 8241,5949 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 8241/827, 5949/209?
Answer: GCF of Numerators as per given numbers 8241/827, 5949/209 is
GCF of Numerators i.e. for 8241,5949 is 3
LCM of denominators i.e. for 827,209 is 172843.
Thus, GCF of Fractions is 3/172843.Finally, GCF of Fractions for 8241/827, 5949/209 is 3/172843.