GCF of 449/22, 584/1578
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 449/22, 584/1578 i.e 1/17358 easily. The following is the detailed procedure to determine the greatest common factor of fractions 449/22, 584/1578.
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 449/22,584/1578?
Given fractions are 449/22,584/1578
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 449/22,584/1578, numerators are 449,584
Denominators are 22,1578
The GCF of 449,584 is 1 .
LCM of 22,1578 is 17358.
The greatest common factor of 449/22,584/1578 = [GCF of 449,584]/[LCM of 22,1578]= 1/17358
Therefore, the GCF of 449/22,584/1578 is 1/17358.
To find the highest common factor of 449,584, 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 584 are 1, 2, 4, 8, 73, 146, 292, 584
The HCF of 449,584 is 1.
Lets's calculate GCF of 449,584
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 449,584 By Matching Biggest Common Factor Method
Now, list down the factors of 449
:1,449
Now, list down the factors of 584
:1,2,4,8,73,146,292,584
Greatest Common Factor
We found the factors 449,584 . The biggest common factor number is the GCF number.
So the greatest common factor 449,584 is 1.
Lets's calculate LCM of 22,1578
| 2 | 22, 1578 |
| 11, 789 |
∴ So the LCM of the given numbers is 2 x 11 x 789 = 17358
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17358
Therefore, the GCF of Fractions 449/22,584/1578 is 1/17358
Least Common Multiple of 22,1578 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 22,1578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(22,1578) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(22,1578) x common factors =2 x 1 = 2
LCM(22,1578) = ( 22 × 1578 ) / 2
LCM(22,1578) = 34716 / 2
LCM(22,1578) = 17358
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FAQs on GCF of Fractions of 449/22, 584/1578
1. What is the HCF of 449,584?
The HCF of 449,584 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 449/22, 584/1578?
Answer: GCF of Numerators as per given numbers 449/22, 584/1578 is
GCF of Numerators i.e. for 449,584 is 1
LCM of denominators i.e. for 22,1578 is 17358.
Thus, GCF of Fractions is 1/17358.Finally, GCF of Fractions for 449/22, 584/1578 is 1/17358.