GCF of 657/289, 5684/171
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 657/289, 5684/171 i.e 1/49419 easily. The following is the detailed procedure to determine the greatest common factor of fractions 657/289, 5684/171.
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 657/289,5684/171?
Given fractions are 657/289,5684/171
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 657/289,5684/171, numerators are 657,5684
Denominators are 289,171
The GCF of 657,5684 is 1 .
LCM of 289,171 is 49419.
The greatest common factor of 657/289,5684/171 = [GCF of 657,5684]/[LCM of 289,171]= 1/49419
Therefore, the GCF of 657/289,5684/171 is 1/49419.
To find the highest common factor of 657,5684, we have to find the factors of both numbers and list the highest common factor.
The factors of 657 are 1, 3, 9, 73, 219, 657
The factors of 5684 are 1, 2, 4, 7, 14, 28, 29, 49, 58, 98, 116, 196, 203, 406, 812, 1421, 2842, 5684
The HCF of 657,5684 is 1.
Lets's calculate GCF of 657,5684
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 657,5684 By Matching Biggest Common Factor Method
Now, list down the factors of 657
:1,3,9,73,219,657
Now, list down the factors of 5684
:1,2,4,7,14,28,29,49,58,98,116,196,203,406,812,1421,2842,5684
Greatest Common Factor
We found the factors 657,5684 . The biggest common factor number is the GCF number.
So the greatest common factor 657,5684 is 1.
Lets's calculate LCM of 289,171
Given numbers has no common factors except 1. So, there LCM is their product i.e 49419
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/49419
Therefore, the GCF of Fractions 657/289,5684/171 is 1/49419
Least Common Multiple of 289,171 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 289,171 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,171) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(289,171) x common factors =1 x 1 = 1
LCM(289,171) = ( 289 × 171 ) / 1
LCM(289,171) = 49419 / 1
LCM(289,171) = 49419
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 657/289, 5684/171
1. What is the HCF of 657,5684?
The HCF of 657,5684 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 657/289, 5684/171?
Answer: GCF of Numerators as per given numbers 657/289, 5684/171 is
GCF of Numerators i.e. for 657,5684 is 1
LCM of denominators i.e. for 289,171 is 49419.
Thus, GCF of Fractions is 1/49419.Finally, GCF of Fractions for 657/289, 5684/171 is 1/49419.