GCF of 489/302, 717/180
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 489/302, 717/180 i.e 3/27180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 489/302, 717/180.
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 489/302,717/180?
Given fractions are 489/302,717/180
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 489/302,717/180, numerators are 489,717
Denominators are 302,180
The GCF of 489,717 is 3 .
LCM of 302,180 is 27180.
The greatest common factor of 489/302,717/180 = [GCF of 489,717]/[LCM of 302,180]= 3/27180
Therefore, the GCF of 489/302,717/180 is 3/27180.
To find the highest common factor of 489,717, we have to find the factors of both numbers and list the highest common factor.
The factors of 489 are 1, 3, 163, 489
The factors of 717 are 1, 3, 239, 717
The HCF of 489,717 is 3.
Lets's calculate GCF of 489,717
| 3 | 489, 717 |
| 163, 239 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 489,717 By Matching Biggest Common Factor Method
Now, list down the factors of 489
:1,3,163,489
Now, list down the factors of 717
:1,3,239,717
Greatest Common Factor
We found the factors 489,717 . The biggest common factor number is the GCF number.
So the greatest common factor 489,717 is 3.
Lets's calculate LCM of 302,180
| 2 | 302, 180 |
| 151, 90 |
∴ So the LCM of the given numbers is 2 x 151 x 90 = 27180
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/27180
Therefore, the GCF of Fractions 489/302,717/180 is 3/27180
Least Common Multiple of 302,180 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 302,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(302,180) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(302,180) x common factors =2 x 1 = 2
LCM(302,180) = ( 302 × 180 ) / 2
LCM(302,180) = 54360 / 2
LCM(302,180) = 27180
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FAQs on GCF of Fractions of 489/302, 717/180
1. What is the HCF of 489,717?
The HCF of 489,717 is 3
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 489/302, 717/180?
Answer: GCF of Numerators as per given numbers 489/302, 717/180 is
GCF of Numerators i.e. for 489,717 is 3
LCM of denominators i.e. for 302,180 is 27180.
Thus, GCF of Fractions is 3/27180.Finally, GCF of Fractions for 489/302, 717/180 is 3/27180.