GCF of 518/24, 309/723
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 518/24, 309/723 i.e 1/5784 easily. The following is the detailed procedure to determine the greatest common factor of fractions 518/24, 309/723.
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 518/24,309/723?
Given fractions are 518/24,309/723
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 518/24,309/723, numerators are 518,309
Denominators are 24,723
The GCF of 518,309 is 1 .
LCM of 24,723 is 5784.
The greatest common factor of 518/24,309/723 = [GCF of 518,309]/[LCM of 24,723]= 1/5784
Therefore, the GCF of 518/24,309/723 is 1/5784.
To find the highest common factor of 518,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 518 are 1, 2, 7, 14, 37, 74, 259, 518
The factors of 309 are 1, 3, 103, 309
The HCF of 518,309 is 1.
Lets's calculate GCF of 518,309
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 518,309 By Matching Biggest Common Factor Method
Now, list down the factors of 518
:1,2,7,14,37,74,259,518
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 518,309 . The biggest common factor number is the GCF number.
So the greatest common factor 518,309 is 1.
Lets's calculate LCM of 24,723
| 3 | 24, 723 |
| 8, 241 |
∴ So the LCM of the given numbers is 3 x 8 x 241 = 5784
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5784
Therefore, the GCF of Fractions 518/24,309/723 is 1/5784
Least Common Multiple of 24,723 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 24,723 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,723) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(24,723) x common factors =3 x 1 = 3
LCM(24,723) = ( 24 × 723 ) / 3
LCM(24,723) = 17352 / 3
LCM(24,723) = 5784
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FAQs on GCF of Fractions of 518/24, 309/723
1. What is the HCF of 518,309?
The HCF of 518,309 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 518/24, 309/723?
Answer: GCF of Numerators as per given numbers 518/24, 309/723 is
GCF of Numerators i.e. for 518,309 is 1
LCM of denominators i.e. for 24,723 is 5784.
Thus, GCF of Fractions is 1/5784.Finally, GCF of Fractions for 518/24, 309/723 is 1/5784.