GCF of 269/35, 401/18, 209/20
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 269/35, 401/18, 209/20 i.e 1/1260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 269/35, 401/18, 209/20.
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 269/35,401/18,209/20?
Given fractions are 269/35,401/18,209/20
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 269/35,401/18,209/20, numerators are 269,401,209
Denominators are 35,18,20
The GCF of 269,401,209 is 1 .
LCM of 35,18,20 is 1260.
The greatest common factor of 269/35,401/18,209/20 = [GCF of 269,401,209]/[LCM of 35,18,20]= 1/1260
Therefore, the GCF of 269/35,401/18,209/20 is 1/1260.
To find the highest common factor of 269,401,209, we have to find the factors of both numbers and list the highest common factor.
The factors of 269 are 1, 269
The factors of 401 are 1, 401
The factors of 209 are 1, 11, 19, 209
The HCF of 269,401,209 is 1.
Lets's calculate GCF of 269,401,209
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 269,401,209 By Matching Biggest Common Factor Method
Now, list down the factors of 269
:1,269
Now, list down the factors of 401
:1,401
Now, list down the factors of 209
:1,11,19,209
Greatest Common Factor
We found the factors 269,401,209 . The biggest common factor number is the GCF number.
So the greatest common factor 269,401,209 is 1.
Lets's calculate LCM of 35,18,20
| 2 | 35, 18, 20 |
| 5 | 35, 9, 10 |
| 7, 9, 2 |
∴ So the LCM of the given numbers is 2 x 5 x 7 x 9 x 2 = 1260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1260
Therefore, the GCF of Fractions 269/35,401/18,209/20 is 1/1260
Least Common Multiple of 35,18,20 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 35,18,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,18,20) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(35,18,20) x common factors =1 x 10 = 10
LCM(35,18,20) = ( 35 × 18 × 20 ) / 10
LCM(35,18,20) = 12600 / 10
LCM(35,18,20) = 1260
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FAQs on GCF of Fractions of 269/35, 401/18, 209/20
1. What is the HCF of 269,401,209?
The HCF of 269,401,209 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 269/35, 401/18, 209/20?
Answer: GCF of Numerators as per given numbers 269/35, 401/18, 209/20 is
GCF of Numerators i.e. for 269,401,209 is 1
LCM of denominators i.e. for 35,18,20 is 1260.
Thus, GCF of Fractions is 1/1260.Finally, GCF of Fractions for 269/35, 401/18, 209/20 is 1/1260.