GCF of 9786/409, 7190/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9786/409, 7190/209 i.e 2/85481 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9786/409, 7190/209.
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 9786/409,7190/209?
Given fractions are 9786/409,7190/209
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 9786/409,7190/209, numerators are 9786,7190
Denominators are 409,209
The GCF of 9786,7190 is 2 .
LCM of 409,209 is 85481.
The greatest common factor of 9786/409,7190/209 = [GCF of 9786,7190]/[LCM of 409,209]= 2/85481
Therefore, the GCF of 9786/409,7190/209 is 2/85481.
To find the highest common factor of 9786,7190, we have to find the factors of both numbers and list the highest common factor.
The factors of 9786 are 1, 2, 3, 6, 7, 14, 21, 42, 233, 466, 699, 1398, 1631, 3262, 4893, 9786
The factors of 7190 are 1, 2, 5, 10, 719, 1438, 3595, 7190
The HCF of 9786,7190 is 2.
Lets's calculate GCF of 9786,7190
| 2 | 9786, 7190 |
| 4893, 3595 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 9786,7190 By Matching Biggest Common Factor Method
Now, list down the factors of 9786
:1,2,3,6,7,14,21,42,233,466,699,1398,1631,3262,4893,9786
Now, list down the factors of 7190
:1,2,5,10,719,1438,3595,7190
Greatest Common Factor
We found the factors 9786,7190 . The biggest common factor number is the GCF number.
So the greatest common factor 9786,7190 is 2.
Lets's calculate LCM of 409,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 85481
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/85481
Therefore, the GCF of Fractions 9786/409,7190/209 is 2/85481
Least Common Multiple of 409,209 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 409,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,209) x common factors =1 x 1 = 1
LCM(409,209) = ( 409 × 209 ) / 1
LCM(409,209) = 85481 / 1
LCM(409,209) = 85481
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FAQs on GCF of Fractions of 9786/409, 7190/209
1. What is the HCF of 9786,7190?
The HCF of 9786,7190 is 2
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 9786/409, 7190/209?
Answer: GCF of Numerators as per given numbers 9786/409, 7190/209 is
GCF of Numerators i.e. for 9786,7190 is 2
LCM of denominators i.e. for 409,209 is 85481.
Thus, GCF of Fractions is 2/85481.Finally, GCF of Fractions for 9786/409, 7190/209 is 2/85481.