GCF of 449/428, 589/418
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 449/428, 589/418 i.e 1/89452 easily. The following is the detailed procedure to determine the greatest common factor of fractions 449/428, 589/418.
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 449/428,589/418?
Given fractions are 449/428,589/418
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 449/428,589/418, numerators are 449,589
Denominators are 428,418
The GCF of 449,589 is 1 .
LCM of 428,418 is 89452.
The greatest common factor of 449/428,589/418 = [GCF of 449,589]/[LCM of 428,418]= 1/89452
Therefore, the GCF of 449/428,589/418 is 1/89452.
To find the highest common factor of 449,589, we have to find the factors of both numbers and list the highest common factor.
The factors of 449 are 1, 449
The factors of 589 are 1, 19, 31, 589
The HCF of 449,589 is 1.
Lets's calculate GCF of 449,589
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 449,589 By Matching Biggest Common Factor Method
Now, list down the factors of 449
:1,449
Now, list down the factors of 589
:1,19,31,589
Greatest Common Factor
We found the factors 449,589 . The biggest common factor number is the GCF number.
So the greatest common factor 449,589 is 1.
Lets's calculate LCM of 428,418
| 2 | 428, 418 |
| 214, 209 |
∴ So the LCM of the given numbers is 2 x 214 x 209 = 89452
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/89452
Therefore, the GCF of Fractions 449/428,589/418 is 1/89452
Least Common Multiple of 428,418 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 428,418 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(428,418) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(428,418) x common factors =2 x 1 = 2
LCM(428,418) = ( 428 × 418 ) / 2
LCM(428,418) = 178904 / 2
LCM(428,418) = 89452
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FAQs on GCF of Fractions of 449/428, 589/418
1. What is the HCF of 449,589?
The HCF of 449,589 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 449/428, 589/418?
Answer: GCF of Numerators as per given numbers 449/428, 589/418 is
GCF of Numerators i.e. for 449,589 is 1
LCM of denominators i.e. for 428,418 is 89452.
Thus, GCF of Fractions is 1/89452.Finally, GCF of Fractions for 449/428, 589/418 is 1/89452.