GCF of 14/203, 68/269, 209/504
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 14/203, 68/269, 209/504 i.e 1/3931704 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/203, 68/269, 209/504.
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 14/203,68/269,209/504?
Given fractions are 14/203,68/269,209/504
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 14/203,68/269,209/504, numerators are 14,68,209
Denominators are 203,269,504
The GCF of 14,68,209 is 1 .
LCM of 203,269,504 is 3931704.
The greatest common factor of 14/203,68/269,209/504 = [GCF of 14,68,209]/[LCM of 203,269,504]= 1/3931704
Therefore, the GCF of 14/203,68/269,209/504 is 1/3931704.
To find the highest common factor of 14,68,209, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 209 are 1, 11, 19, 209
The HCF of 14,68,209 is 1.
Lets's calculate GCF of 14,68,209
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 14,68,209 By Matching Biggest Common Factor Method
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 209
:1,11,19,209
Greatest Common Factor
We found the factors 14,68,209 . The biggest common factor number is the GCF number.
So the greatest common factor 14,68,209 is 1.
Lets's calculate LCM of 203,269,504
| 7 | 203, 269, 504 |
| 29, 269, 72 |
∴ So the LCM of the given numbers is 7 x 29 x 269 x 72 = 3931704
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3931704
Therefore, the GCF of Fractions 14/203,68/269,209/504 is 1/3931704
Least Common Multiple of 203,269,504 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 203,269,504 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(203,269,504) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(203,269,504) x common factors =1 x 7 = 7
LCM(203,269,504) = ( 203 × 269 × 504 ) / 7
LCM(203,269,504) = 27521928 / 7
LCM(203,269,504) = 3931704
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FAQs on GCF of Fractions of 14/203, 68/269, 209/504
1. What is the HCF of 14,68,209?
The HCF of 14,68,209 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 14/203, 68/269, 209/504?
Answer: GCF of Numerators as per given numbers 14/203, 68/269, 209/504 is
GCF of Numerators i.e. for 14,68,209 is 1
LCM of denominators i.e. for 203,269,504 is 3931704.
Thus, GCF of Fractions is 1/3931704.Finally, GCF of Fractions for 14/203, 68/269, 209/504 is 1/3931704.