GCF of 171/54, 309/374
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 171/54, 309/374 i.e 3/10098 easily. The following is the detailed procedure to determine the greatest common factor of fractions 171/54, 309/374.
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 171/54,309/374?
Given fractions are 171/54,309/374
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 171/54,309/374, numerators are 171,309
Denominators are 54,374
The GCF of 171,309 is 3 .
LCM of 54,374 is 10098.
The greatest common factor of 171/54,309/374 = [GCF of 171,309]/[LCM of 54,374]= 3/10098
Therefore, the GCF of 171/54,309/374 is 3/10098.
To find the highest common factor of 171,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 171 are 1, 3, 9, 19, 57, 171
The factors of 309 are 1, 3, 103, 309
The HCF of 171,309 is 3.
Lets's calculate GCF of 171,309
| 3 | 171, 309 |
| 57, 103 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 171,309 By Matching Biggest Common Factor Method
Now, list down the factors of 171
:1,3,9,19,57,171
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 171,309 . The biggest common factor number is the GCF number.
So the greatest common factor 171,309 is 3.
Lets's calculate LCM of 54,374
| 2 | 54, 374 |
| 27, 187 |
∴ So the LCM of the given numbers is 2 x 27 x 187 = 10098
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/10098
Therefore, the GCF of Fractions 171/54,309/374 is 3/10098
Least Common Multiple of 54,374 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 54,374 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,374) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(54,374) x common factors =2 x 1 = 2
LCM(54,374) = ( 54 × 374 ) / 2
LCM(54,374) = 20196 / 2
LCM(54,374) = 10098
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FAQs on GCF of Fractions of 171/54, 309/374
1. What is the HCF of 171,309?
The HCF of 171,309 is 3
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 171/54, 309/374?
Answer: GCF of Numerators as per given numbers 171/54, 309/374 is
GCF of Numerators i.e. for 171,309 is 3
LCM of denominators i.e. for 54,374 is 10098.
Thus, GCF of Fractions is 3/10098.Finally, GCF of Fractions for 171/54, 309/374 is 3/10098.