GCF of 209/29, 274/33, 159/16
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 209/29, 274/33, 159/16 i.e 1/15312 easily. The following is the detailed procedure to determine the greatest common factor of fractions 209/29, 274/33, 159/16.
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 209/29,274/33,159/16?
Given fractions are 209/29,274/33,159/16
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 209/29,274/33,159/16, numerators are 209,274,159
Denominators are 29,33,16
The GCF of 209,274,159 is 1 .
LCM of 29,33,16 is 15312.
The greatest common factor of 209/29,274/33,159/16 = [GCF of 209,274,159]/[LCM of 29,33,16]= 1/15312
Therefore, the GCF of 209/29,274/33,159/16 is 1/15312.
To find the highest common factor of 209,274,159, we have to find the factors of both numbers and list the highest common factor.
The factors of 209 are 1, 11, 19, 209
The factors of 274 are 1, 2, 137, 274
The factors of 159 are 1, 3, 53, 159
The HCF of 209,274,159 is 1.
Lets's calculate GCF of 209,274,159
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 209,274,159 By Matching Biggest Common Factor Method
Now, list down the factors of 209
:1,11,19,209
Now, list down the factors of 274
:1,2,137,274
Now, list down the factors of 159
:1,3,53,159
Greatest Common Factor
We found the factors 209,274,159 . The biggest common factor number is the GCF number.
So the greatest common factor 209,274,159 is 1.
Lets's calculate LCM of 29,33,16
Given numbers has no common factors except 1. So, there LCM is their product i.e 15312
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/15312
Therefore, the GCF of Fractions 209/29,274/33,159/16 is 1/15312
Least Common Multiple of 29,33,16 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 29,33,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(29,33,16) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(29,33,16) x common factors =1 x 1 = 1
LCM(29,33,16) = ( 29 × 33 × 16 ) / 1
LCM(29,33,16) = 15312 / 1
LCM(29,33,16) = 15312
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FAQs on GCF of Fractions of 209/29, 274/33, 159/16
1. What is the HCF of 209,274,159?
The HCF of 209,274,159 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 209/29, 274/33, 159/16?
Answer: GCF of Numerators as per given numbers 209/29, 274/33, 159/16 is
GCF of Numerators i.e. for 209,274,159 is 1
LCM of denominators i.e. for 29,33,16 is 15312.
Thus, GCF of Fractions is 1/15312.Finally, GCF of Fractions for 209/29, 274/33, 159/16 is 1/15312.