GCF of 589/416, 478/470
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 589/416, 478/470 i.e 1/97760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 589/416, 478/470.
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 589/416,478/470?
Given fractions are 589/416,478/470
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 589/416,478/470, numerators are 589,478
Denominators are 416,470
The GCF of 589,478 is 1 .
LCM of 416,470 is 97760.
The greatest common factor of 589/416,478/470 = [GCF of 589,478]/[LCM of 416,470]= 1/97760
Therefore, the GCF of 589/416,478/470 is 1/97760.
To find the highest common factor of 589,478, we have to find the factors of both numbers and list the highest common factor.
The factors of 589 are 1, 19, 31, 589
The factors of 478 are 1, 2, 239, 478
The HCF of 589,478 is 1.
Lets's calculate GCF of 589,478
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 589,478 By Matching Biggest Common Factor Method
Now, list down the factors of 589
:1,19,31,589
Now, list down the factors of 478
:1,2,239,478
Greatest Common Factor
We found the factors 589,478 . The biggest common factor number is the GCF number.
So the greatest common factor 589,478 is 1.
Lets's calculate LCM of 416,470
| 2 | 416, 470 |
| 208, 235 |
∴ So the LCM of the given numbers is 2 x 208 x 235 = 97760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/97760
Therefore, the GCF of Fractions 589/416,478/470 is 1/97760
Least Common Multiple of 416,470 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 416,470 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(416,470) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(416,470) x common factors =2 x 1 = 2
LCM(416,470) = ( 416 × 470 ) / 2
LCM(416,470) = 195520 / 2
LCM(416,470) = 97760
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FAQs on GCF of Fractions of 589/416, 478/470
1. What is the HCF of 589,478?
The HCF of 589,478 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 589/416, 478/470?
Answer: GCF of Numerators as per given numbers 589/416, 478/470 is
GCF of Numerators i.e. for 589,478 is 1
LCM of denominators i.e. for 416,470 is 97760.
Thus, GCF of Fractions is 1/97760.Finally, GCF of Fractions for 589/416, 478/470 is 1/97760.