GCF of 2009/258, 6705/7870
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2009/258, 6705/7870 i.e 1/1015230 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2009/258, 6705/7870.
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 2009/258,6705/7870?
Given fractions are 2009/258,6705/7870
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 2009/258,6705/7870, numerators are 2009,6705
Denominators are 258,7870
The GCF of 2009,6705 is 1 .
LCM of 258,7870 is 1015230.
The greatest common factor of 2009/258,6705/7870 = [GCF of 2009,6705]/[LCM of 258,7870]= 1/1015230
Therefore, the GCF of 2009/258,6705/7870 is 1/1015230.
To find the highest common factor of 2009,6705, we have to find the factors of both numbers and list the highest common factor.
The factors of 2009 are 1, 7, 41, 49, 287, 2009
The factors of 6705 are 1, 3, 5, 9, 15, 45, 149, 447, 745, 1341, 2235, 6705
The HCF of 2009,6705 is 1.
Lets's calculate GCF of 2009,6705
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2009,6705 By Matching Biggest Common Factor Method
Now, list down the factors of 2009
:1,7,41,49,287,2009
Now, list down the factors of 6705
:1,3,5,9,15,45,149,447,745,1341,2235,6705
Greatest Common Factor
We found the factors 2009,6705 . The biggest common factor number is the GCF number.
So the greatest common factor 2009,6705 is 1.
Lets's calculate LCM of 258,7870
| 2 | 258, 7870 |
| 129, 3935 |
∴ So the LCM of the given numbers is 2 x 129 x 3935 = 1015230
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1015230
Therefore, the GCF of Fractions 2009/258,6705/7870 is 1/1015230
Least Common Multiple of 258,7870 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 258,7870 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(258,7870) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(258,7870) x common factors =2 x 1 = 2
LCM(258,7870) = ( 258 × 7870 ) / 2
LCM(258,7870) = 2030460 / 2
LCM(258,7870) = 1015230
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FAQs on GCF of Fractions of 2009/258, 6705/7870
1. What is the HCF of 2009,6705?
The HCF of 2009,6705 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 2009/258, 6705/7870?
Answer: GCF of Numerators as per given numbers 2009/258, 6705/7870 is
GCF of Numerators i.e. for 2009,6705 is 1
LCM of denominators i.e. for 258,7870 is 1015230.
Thus, GCF of Fractions is 1/1015230.Finally, GCF of Fractions for 2009/258, 6705/7870 is 1/1015230.