GCF of 560/20, 512/497
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 560/20, 512/497 i.e 16/9940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 560/20, 512/497.
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 560/20,512/497?
Given fractions are 560/20,512/497
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 560/20,512/497, numerators are 560,512
Denominators are 20,497
The GCF of 560,512 is 16 .
LCM of 20,497 is 9940.
The greatest common factor of 560/20,512/497 = [GCF of 560,512]/[LCM of 20,497]= 16/9940
Therefore, the GCF of 560/20,512/497 is 16/9940.
To find the highest common factor of 560,512, 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 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 560,512 is 16.
Lets's calculate GCF of 560,512
| 2 | 560, 512 |
| 2 | 280, 256 |
| 2 | 140, 128 |
| 2 | 70, 64 |
| 35, 32 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Greatest Common Factor of 560,512 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 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 560,512 . The biggest common factor number is the GCF number.
So the greatest common factor 560,512 is 16.
Lets's calculate LCM of 20,497
Given numbers has no common factors except 1. So, there LCM is their product i.e 9940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/9940
Therefore, the GCF of Fractions 560/20,512/497 is 16/9940
Least Common Multiple of 20,497 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 20,497 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,497) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(20,497) x common factors =1 x 1 = 1
LCM(20,497) = ( 20 × 497 ) / 1
LCM(20,497) = 9940 / 1
LCM(20,497) = 9940
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FAQs on GCF of Fractions of 560/20, 512/497
1. What is the HCF of 560,512?
The HCF of 560,512 is 16
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 560/20, 512/497?
Answer: GCF of Numerators as per given numbers 560/20, 512/497 is
GCF of Numerators i.e. for 560,512 is 16
LCM of denominators i.e. for 20,497 is 9940.
Thus, GCF of Fractions is 16/9940.Finally, GCF of Fractions for 560/20, 512/497 is 16/9940.