GCF of 194/458, 649/409
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 194/458, 649/409 i.e 1/187322 easily. The following is the detailed procedure to determine the greatest common factor of fractions 194/458, 649/409.
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 194/458,649/409?
Given fractions are 194/458,649/409
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 194/458,649/409, numerators are 194,649
Denominators are 458,409
The GCF of 194,649 is 1 .
LCM of 458,409 is 187322.
The greatest common factor of 194/458,649/409 = [GCF of 194,649]/[LCM of 458,409]= 1/187322
Therefore, the GCF of 194/458,649/409 is 1/187322.
To find the highest common factor of 194,649, we have to find the factors of both numbers and list the highest common factor.
The factors of 194 are 1, 2, 97, 194
The factors of 649 are 1, 11, 59, 649
The HCF of 194,649 is 1.
Lets's calculate GCF of 194,649
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 194,649 By Matching Biggest Common Factor Method
Now, list down the factors of 194
:1,2,97,194
Now, list down the factors of 649
:1,11,59,649
Greatest Common Factor
We found the factors 194,649 . The biggest common factor number is the GCF number.
So the greatest common factor 194,649 is 1.
Lets's calculate LCM of 458,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 187322
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/187322
Therefore, the GCF of Fractions 194/458,649/409 is 1/187322
Least Common Multiple of 458,409 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 458,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(458,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(458,409) x common factors =1 x 1 = 1
LCM(458,409) = ( 458 × 409 ) / 1
LCM(458,409) = 187322 / 1
LCM(458,409) = 187322
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FAQs on GCF of Fractions of 194/458, 649/409
1. What is the HCF of 194,649?
The HCF of 194,649 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 194/458, 649/409?
Answer: GCF of Numerators as per given numbers 194/458, 649/409 is
GCF of Numerators i.e. for 194,649 is 1
LCM of denominators i.e. for 458,409 is 187322.
Thus, GCF of Fractions is 1/187322.Finally, GCF of Fractions for 194/458, 649/409 is 1/187322.