GCF of 382/69, 209/409
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 382/69, 209/409 i.e 1/28221 easily. The following is the detailed procedure to determine the greatest common factor of fractions 382/69, 209/409.
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 382/69,209/409?
Given fractions are 382/69,209/409
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 382/69,209/409, numerators are 382,209
Denominators are 69,409
The GCF of 382,209 is 1 .
LCM of 69,409 is 28221.
The greatest common factor of 382/69,209/409 = [GCF of 382,209]/[LCM of 69,409]= 1/28221
Therefore, the GCF of 382/69,209/409 is 1/28221.
To find the highest common factor of 382,209, we have to find the factors of both numbers and list the highest common factor.
The factors of 382 are 1, 2, 191, 382
The factors of 209 are 1, 11, 19, 209
The HCF of 382,209 is 1.
Lets's calculate GCF of 382,209
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 382,209 By Matching Biggest Common Factor Method
Now, list down the factors of 382
:1,2,191,382
Now, list down the factors of 209
:1,11,19,209
Greatest Common Factor
We found the factors 382,209 . The biggest common factor number is the GCF number.
So the greatest common factor 382,209 is 1.
Lets's calculate LCM of 69,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 28221
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28221
Therefore, the GCF of Fractions 382/69,209/409 is 1/28221
Least Common Multiple of 69,409 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 69,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(69,409) x common factors =1 x 1 = 1
LCM(69,409) = ( 69 × 409 ) / 1
LCM(69,409) = 28221 / 1
LCM(69,409) = 28221
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 382/69, 209/409
1. What is the HCF of 382,209?
The HCF of 382,209 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 382/69, 209/409?
Answer: GCF of Numerators as per given numbers 382/69, 209/409 is
GCF of Numerators i.e. for 382,209 is 1
LCM of denominators i.e. for 69,409 is 28221.
Thus, GCF of Fractions is 1/28221.Finally, GCF of Fractions for 382/69, 209/409 is 1/28221.