GCF of 580/586, 410/729
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 580/586, 410/729 i.e 10/427194 easily. The following is the detailed procedure to determine the greatest common factor of fractions 580/586, 410/729.
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 580/586,410/729?
Given fractions are 580/586,410/729
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 580/586,410/729, numerators are 580,410
Denominators are 586,729
The GCF of 580,410 is 10 .
LCM of 586,729 is 427194.
The greatest common factor of 580/586,410/729 = [GCF of 580,410]/[LCM of 586,729]= 10/427194
Therefore, the GCF of 580/586,410/729 is 10/427194.
To find the highest common factor of 580,410, we have to find the factors of both numbers and list the highest common factor.
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The HCF of 580,410 is 10.
Lets's calculate GCF of 580,410
| 2 | 580, 410 |
| 5 | 290, 205 |
| 58, 41 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 580,410 By Matching Biggest Common Factor Method
Now, list down the factors of 580
:1,2,4,5,10,20,29,58,116,145,290,580
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Greatest Common Factor
We found the factors 580,410 . The biggest common factor number is the GCF number.
So the greatest common factor 580,410 is 10.
Lets's calculate LCM of 586,729
Given numbers has no common factors except 1. So, there LCM is their product i.e 427194
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/427194
Therefore, the GCF of Fractions 580/586,410/729 is 10/427194
Least Common Multiple of 586,729 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 586,729 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(586,729) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(586,729) x common factors =1 x 1 = 1
LCM(586,729) = ( 586 × 729 ) / 1
LCM(586,729) = 427194 / 1
LCM(586,729) = 427194
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FAQs on GCF of Fractions of 580/586, 410/729
1. What is the HCF of 580,410?
The HCF of 580,410 is 10
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 580/586, 410/729?
Answer: GCF of Numerators as per given numbers 580/586, 410/729 is
GCF of Numerators i.e. for 580,410 is 10
LCM of denominators i.e. for 586,729 is 427194.
Thus, GCF of Fractions is 10/427194.Finally, GCF of Fractions for 580/586, 410/729 is 10/427194.