GCF of 560/504, 590/309
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 560/504, 590/309 i.e 10/51912 easily. The following is the detailed procedure to determine the greatest common factor of fractions 560/504, 590/309.
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 560/504,590/309?
Given fractions are 560/504,590/309
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 560/504,590/309, numerators are 560,590
Denominators are 504,309
The GCF of 560,590 is 10 .
LCM of 504,309 is 51912.
The greatest common factor of 560/504,590/309 = [GCF of 560,590]/[LCM of 504,309]= 10/51912
Therefore, the GCF of 560/504,590/309 is 10/51912.
To find the highest common factor of 560,590, we have to find the factors of both numbers and list the highest common factor.
The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The factors of 590 are 1, 2, 5, 10, 59, 118, 295, 590
The HCF of 560,590 is 10.
Lets's calculate GCF of 560,590
| 2 | 560, 590 |
| 5 | 280, 295 |
| 56, 59 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 560,590 By Matching Biggest Common Factor Method
Now, list down the factors of 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Now, list down the factors of 590
:1,2,5,10,59,118,295,590
Greatest Common Factor
We found the factors 560,590 . The biggest common factor number is the GCF number.
So the greatest common factor 560,590 is 10.
Lets's calculate LCM of 504,309
| 3 | 504, 309 |
| 168, 103 |
∴ So the LCM of the given numbers is 3 x 168 x 103 = 51912
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/51912
Therefore, the GCF of Fractions 560/504,590/309 is 10/51912
Least Common Multiple of 504,309 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 504,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(504,309) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(504,309) x common factors =3 x 1 = 3
LCM(504,309) = ( 504 × 309 ) / 3
LCM(504,309) = 155736 / 3
LCM(504,309) = 51912
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FAQs on GCF of Fractions of 560/504, 590/309
1. What is the HCF of 560,590?
The HCF of 560,590 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 560/504, 590/309?
Answer: GCF of Numerators as per given numbers 560/504, 590/309 is
GCF of Numerators i.e. for 560,590 is 10
LCM of denominators i.e. for 504,309 is 51912.
Thus, GCF of Fractions is 10/51912.Finally, GCF of Fractions for 560/504, 590/309 is 10/51912.