Use our free GCF of Fractions Calculator tool to compute the GCF of 560/406, 384/195 i.e 16/79170 easily. The following is the detailed procedure to determine the greatest common factor of fractions 560/406, 384/195.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 560/406,384/195
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 560/406,384/195, numerators are 560,384
Denominators are 406,195
The GCF of 560,384 is 16 .
LCM of 406,195 is 79170.
The greatest common factor of 560/406,384/195 = [GCF of 560,384]/[LCM of 406,195]= 16/79170
Therefore, the GCF of 560/406,384/195 is 16/79170.
To find the highest common factor of 560,384, 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 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The HCF of 560,384 is 16.
Lets's calculate GCF of 560,384
2 | 560, 384 |
2 | 280, 192 |
2 | 140, 96 |
2 | 70, 48 |
35, 24 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
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 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Greatest Common Factor
We found the factors 560,384 . The biggest common factor number is the GCF number.
So the greatest common factor 560,384 is 16.
Lets's calculate LCM of 406,195
Given numbers has no common factors except 1. So, there LCM is their product i.e 79170
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/79170
Therefore, the GCF of Fractions 560/406,384/195 is 16/79170
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 406,195 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,195) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(406,195) x common factors =1 x 1 = 1
LCM(406,195) = ( 406 × 195 ) / 1
LCM(406,195) = 79170 / 1
LCM(406,195) = 79170
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 560,384?
The HCF of 560,384 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 560/406, 384/195?
Answer: GCF of Numerators as per given numbers 560/406, 384/195 is
GCF of Numerators i.e. for 560,384 is 16
LCM of denominators i.e. for 406,195 is 79170.
Thus, GCF of Fractions is 16/79170.Finally, GCF of Fractions for 560/406, 384/195 is 16/79170.