GCF of 582/75, 470/5800
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 582/75, 470/5800 i.e 2/17400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 582/75, 470/5800.
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 582/75,470/5800?
Given fractions are 582/75,470/5800
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 582/75,470/5800, numerators are 582,470
Denominators are 75,5800
The GCF of 582,470 is 2 .
LCM of 75,5800 is 17400.
The greatest common factor of 582/75,470/5800 = [GCF of 582,470]/[LCM of 75,5800]= 2/17400
Therefore, the GCF of 582/75,470/5800 is 2/17400.
To find the highest common factor of 582,470, we have to find the factors of both numbers and list the highest common factor.
The factors of 582 are 1, 2, 3, 6, 97, 194, 291, 582
The factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470
The HCF of 582,470 is 2.
Lets's calculate GCF of 582,470
| 2 | 582, 470 |
| 291, 235 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 582,470 By Matching Biggest Common Factor Method
Now, list down the factors of 582
:1,2,3,6,97,194,291,582
Now, list down the factors of 470
:1,2,5,10,47,94,235,470
Greatest Common Factor
We found the factors 582,470 . The biggest common factor number is the GCF number.
So the greatest common factor 582,470 is 2.
Lets's calculate LCM of 75,5800
| 5 | 75, 5800 |
| 5 | 15, 1160 |
| 3, 232 |
∴ So the LCM of the given numbers is 5 x 5 x 3 x 232 = 17400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/17400
Therefore, the GCF of Fractions 582/75,470/5800 is 2/17400
Least Common Multiple of 75,5800 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 75,5800 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,5800) = 25
common factors(in case of two or more numbers have common factors) = 1
GCF(75,5800) x common factors =25 x 1 = 25
LCM(75,5800) = ( 75 × 5800 ) / 25
LCM(75,5800) = 435000 / 25
LCM(75,5800) = 17400
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FAQs on GCF of Fractions of 582/75, 470/5800
1. What is the HCF of 582,470?
The HCF of 582,470 is 2
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 582/75, 470/5800?
Answer: GCF of Numerators as per given numbers 582/75, 470/5800 is
GCF of Numerators i.e. for 582,470 is 2
LCM of denominators i.e. for 75,5800 is 17400.
Thus, GCF of Fractions is 2/17400.Finally, GCF of Fractions for 582/75, 470/5800 is 2/17400.