GCF of 814/52, 171/309
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 814/52, 171/309 i.e 1/16068 easily. The following is the detailed procedure to determine the greatest common factor of fractions 814/52, 171/309.
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 814/52,171/309?
Given fractions are 814/52,171/309
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 814/52,171/309, numerators are 814,171
Denominators are 52,309
The GCF of 814,171 is 1 .
LCM of 52,309 is 16068.
The greatest common factor of 814/52,171/309 = [GCF of 814,171]/[LCM of 52,309]= 1/16068
Therefore, the GCF of 814/52,171/309 is 1/16068.
To find the highest common factor of 814,171, we have to find the factors of both numbers and list the highest common factor.
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The factors of 171 are 1, 3, 9, 19, 57, 171
The HCF of 814,171 is 1.
Lets's calculate GCF of 814,171
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 814,171 By Matching Biggest Common Factor Method
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Now, list down the factors of 171
:1,3,9,19,57,171
Greatest Common Factor
We found the factors 814,171 . The biggest common factor number is the GCF number.
So the greatest common factor 814,171 is 1.
Lets's calculate LCM of 52,309
Given numbers has no common factors except 1. So, there LCM is their product i.e 16068
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16068
Therefore, the GCF of Fractions 814/52,171/309 is 1/16068
Least Common Multiple of 52,309 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 52,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(52,309) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(52,309) x common factors =1 x 1 = 1
LCM(52,309) = ( 52 × 309 ) / 1
LCM(52,309) = 16068 / 1
LCM(52,309) = 16068
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FAQs on GCF of Fractions of 814/52, 171/309
1. What is the HCF of 814,171?
The HCF of 814,171 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 814/52, 171/309?
Answer: GCF of Numerators as per given numbers 814/52, 171/309 is
GCF of Numerators i.e. for 814,171 is 1
LCM of denominators i.e. for 52,309 is 16068.
Thus, GCF of Fractions is 1/16068.Finally, GCF of Fractions for 814/52, 171/309 is 1/16068.