GCF of 381/810, 209/984
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 381/810, 209/984 i.e 1/132840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 381/810, 209/984.
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 381/810,209/984?
Given fractions are 381/810,209/984
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 381/810,209/984, numerators are 381,209
Denominators are 810,984
The GCF of 381,209 is 1 .
LCM of 810,984 is 132840.
The greatest common factor of 381/810,209/984 = [GCF of 381,209]/[LCM of 810,984]= 1/132840
Therefore, the GCF of 381/810,209/984 is 1/132840.
To find the highest common factor of 381,209, we have to find the factors of both numbers and list the highest common factor.
The factors of 381 are 1, 3, 127, 381
The factors of 209 are 1, 11, 19, 209
The HCF of 381,209 is 1.
Lets's calculate GCF of 381,209
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 381,209 By Matching Biggest Common Factor Method
Now, list down the factors of 381
:1,3,127,381
Now, list down the factors of 209
:1,11,19,209
Greatest Common Factor
We found the factors 381,209 . The biggest common factor number is the GCF number.
So the greatest common factor 381,209 is 1.
Lets's calculate LCM of 810,984
| 2 | 810, 984 |
| 3 | 405, 492 |
| 135, 164 |
∴ So the LCM of the given numbers is 2 x 3 x 135 x 164 = 132840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/132840
Therefore, the GCF of Fractions 381/810,209/984 is 1/132840
Least Common Multiple of 810,984 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 810,984 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(810,984) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(810,984) x common factors =6 x 1 = 6
LCM(810,984) = ( 810 × 984 ) / 6
LCM(810,984) = 797040 / 6
LCM(810,984) = 132840
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FAQs on GCF of Fractions of 381/810, 209/984
1. What is the HCF of 381,209?
The HCF of 381,209 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 381/810, 209/984?
Answer: GCF of Numerators as per given numbers 381/810, 209/984 is
GCF of Numerators i.e. for 381,209 is 1
LCM of denominators i.e. for 810,984 is 132840.
Thus, GCF of Fractions is 1/132840.Finally, GCF of Fractions for 381/810, 209/984 is 1/132840.