Use our free GCF of Fractions Calculator tool to compute the GCF of 589/270, 318/540 i.e 1/540 easily. The following is the detailed procedure to determine the greatest common factor of fractions 589/270, 318/540.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 589/270,318/540
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 589/270,318/540, numerators are 589,318
Denominators are 270,540
The GCF of 589,318 is 1 .
LCM of 270,540 is 540.
The greatest common factor of 589/270,318/540 = [GCF of 589,318]/[LCM of 270,540]= 1/540
Therefore, the GCF of 589/270,318/540 is 1/540.
To find the highest common factor of 589,318, we have to find the factors of both numbers and list the highest common factor.
The factors of 589 are 1, 19, 31, 589
The factors of 318 are 1, 2, 3, 6, 53, 106, 159, 318
The HCF of 589,318 is 1.
Lets's calculate GCF of 589,318
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 589
:1,19,31,589
Now, list down the factors of 318
:1,2,3,6,53,106,159,318
Greatest Common Factor
We found the factors 589,318 . The biggest common factor number is the GCF number.
So the greatest common factor 589,318 is 1.
Lets's calculate LCM of 270,540
2 | 270, 540 |
3 | 135, 270 |
3 | 45, 90 |
3 | 15, 30 |
5 | 5, 10 |
1, 2 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 5 x 1 x 2 = 540
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/540
Therefore, the GCF of Fractions 589/270,318/540 is 1/540
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 270,540 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(270,540) = 270
common factors(in case of two or more numbers have common factors) = 1
GCF(270,540) x common factors =270 x 1 = 270
LCM(270,540) = ( 270 × 540 ) / 270
LCM(270,540) = 145800 / 270
LCM(270,540) = 540
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 589,318?
The HCF of 589,318 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 589/270, 318/540?
Answer: GCF of Numerators as per given numbers 589/270, 318/540 is
GCF of Numerators i.e. for 589,318 is 1
LCM of denominators i.e. for 270,540 is 540.
Thus, GCF of Fractions is 1/540.Finally, GCF of Fractions for 589/270, 318/540 is 1/540.