GCF of 321/408, 584/285
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 321/408, 584/285 i.e 1/38760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 321/408, 584/285.
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 321/408,584/285?
Given fractions are 321/408,584/285
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 321/408,584/285, numerators are 321,584
Denominators are 408,285
The GCF of 321,584 is 1 .
LCM of 408,285 is 38760.
The greatest common factor of 321/408,584/285 = [GCF of 321,584]/[LCM of 408,285]= 1/38760
Therefore, the GCF of 321/408,584/285 is 1/38760.
To find the highest common factor of 321,584, we have to find the factors of both numbers and list the highest common factor.
The factors of 321 are 1, 3, 107, 321
The factors of 584 are 1, 2, 4, 8, 73, 146, 292, 584
The HCF of 321,584 is 1.
Lets's calculate GCF of 321,584
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 321,584 By Matching Biggest Common Factor Method
Now, list down the factors of 321
:1,3,107,321
Now, list down the factors of 584
:1,2,4,8,73,146,292,584
Greatest Common Factor
We found the factors 321,584 . The biggest common factor number is the GCF number.
So the greatest common factor 321,584 is 1.
Lets's calculate LCM of 408,285
| 3 | 408, 285 |
| 136, 95 |
∴ So the LCM of the given numbers is 3 x 136 x 95 = 38760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/38760
Therefore, the GCF of Fractions 321/408,584/285 is 1/38760
Least Common Multiple of 408,285 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 408,285 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(408,285) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(408,285) x common factors =3 x 1 = 3
LCM(408,285) = ( 408 × 285 ) / 3
LCM(408,285) = 116280 / 3
LCM(408,285) = 38760
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FAQs on GCF of Fractions of 321/408, 584/285
1. What is the HCF of 321,584?
The HCF of 321,584 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 321/408, 584/285?
Answer: GCF of Numerators as per given numbers 321/408, 584/285 is
GCF of Numerators i.e. for 321,584 is 1
LCM of denominators i.e. for 408,285 is 38760.
Thus, GCF of Fractions is 1/38760.Finally, GCF of Fractions for 321/408, 584/285 is 1/38760.