Use our free GCF of Fractions Calculator tool to compute the GCF of 564/298, 390/595 i.e 6/177310 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/298, 390/595.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 564/298,390/595
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 564/298,390/595, numerators are 564,390
Denominators are 298,595
The GCF of 564,390 is 6 .
LCM of 298,595 is 177310.
The greatest common factor of 564/298,390/595 = [GCF of 564,390]/[LCM of 298,595]= 6/177310
Therefore, the GCF of 564/298,390/595 is 6/177310.
To find the highest common factor of 564,390, we have to find the factors of both numbers and list the highest common factor.
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390
The HCF of 564,390 is 6.
Lets's calculate GCF of 564,390
2 | 564, 390 |
3 | 282, 195 |
94, 65 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Now, list down the factors of 390
:1,2,3,5,6,10,13,15,26,30,39,65,78,130,195,390
Greatest Common Factor
We found the factors 564,390 . The biggest common factor number is the GCF number.
So the greatest common factor 564,390 is 6.
Lets's calculate LCM of 298,595
Given numbers has no common factors except 1. So, there LCM is their product i.e 177310
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/177310
Therefore, the GCF of Fractions 564/298,390/595 is 6/177310
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 298,595 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(298,595) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(298,595) x common factors =1 x 1 = 1
LCM(298,595) = ( 298 × 595 ) / 1
LCM(298,595) = 177310 / 1
LCM(298,595) = 177310
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 564,390?
The HCF of 564,390 is 6
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 564/298, 390/595?
Answer: GCF of Numerators as per given numbers 564/298, 390/595 is
GCF of Numerators i.e. for 564,390 is 6
LCM of denominators i.e. for 298,595 is 177310.
Thus, GCF of Fractions is 6/177310.Finally, GCF of Fractions for 564/298, 390/595 is 6/177310.