GCF of 2059/213, 8206/3657
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2059/213, 8206/3657 i.e 1/259647 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2059/213, 8206/3657.
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 2059/213,8206/3657?
Given fractions are 2059/213,8206/3657
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 2059/213,8206/3657, numerators are 2059,8206
Denominators are 213,3657
The GCF of 2059,8206 is 1 .
LCM of 213,3657 is 259647.
The greatest common factor of 2059/213,8206/3657 = [GCF of 2059,8206]/[LCM of 213,3657]= 1/259647
Therefore, the GCF of 2059/213,8206/3657 is 1/259647.
To find the highest common factor of 2059,8206, we have to find the factors of both numbers and list the highest common factor.
The factors of 2059 are 1, 29, 71, 2059
The factors of 8206 are 1, 2, 11, 22, 373, 746, 4103, 8206
The HCF of 2059,8206 is 1.
Lets's calculate GCF of 2059,8206
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2059,8206 By Matching Biggest Common Factor Method
Now, list down the factors of 2059
:1,29,71,2059
Now, list down the factors of 8206
:1,2,11,22,373,746,4103,8206
Greatest Common Factor
We found the factors 2059,8206 . The biggest common factor number is the GCF number.
So the greatest common factor 2059,8206 is 1.
Lets's calculate LCM of 213,3657
| 3 | 213, 3657 |
| 71, 1219 |
∴ So the LCM of the given numbers is 3 x 71 x 1219 = 259647
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/259647
Therefore, the GCF of Fractions 2059/213,8206/3657 is 1/259647
Least Common Multiple of 213,3657 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 213,3657 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(213,3657) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(213,3657) x common factors =3 x 1 = 3
LCM(213,3657) = ( 213 × 3657 ) / 3
LCM(213,3657) = 778941 / 3
LCM(213,3657) = 259647
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FAQs on GCF of Fractions of 2059/213, 8206/3657
1. What is the HCF of 2059,8206?
The HCF of 2059,8206 is 1
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 2059/213, 8206/3657?
Answer: GCF of Numerators as per given numbers 2059/213, 8206/3657 is
GCF of Numerators i.e. for 2059,8206 is 1
LCM of denominators i.e. for 213,3657 is 259647.
Thus, GCF of Fractions is 1/259647.Finally, GCF of Fractions for 2059/213, 8206/3657 is 1/259647.