Use our free GCF of Fractions Calculator tool to compute the GCF of 540/585, 640/590 i.e 20/69030 easily. The following is the detailed procedure to determine the greatest common factor of fractions 540/585, 640/590.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 540/585,640/590
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 540/585,640/590, numerators are 540,640
Denominators are 585,590
The GCF of 540,640 is 20 .
LCM of 585,590 is 69030.
The greatest common factor of 540/585,640/590 = [GCF of 540,640]/[LCM of 585,590]= 20/69030
Therefore, the GCF of 540/585,640/590 is 20/69030.
To find the highest common factor of 540,640, we have to find the factors of both numbers and list the highest common factor.
The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
The factors of 640 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640
The HCF of 540,640 is 20.
Lets's calculate GCF of 540,640
2 | 540, 640 |
2 | 270, 320 |
5 | 135, 160 |
27, 32 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Now, list down the factors of 540
:1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
Now, list down the factors of 640
:1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640
Greatest Common Factor
We found the factors 540,640 . The biggest common factor number is the GCF number.
So the greatest common factor 540,640 is 20.
Lets's calculate LCM of 585,590
5 | 585, 590 |
117, 118 |
∴ So the LCM of the given numbers is 5 x 117 x 118 = 69030
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/69030
Therefore, the GCF of Fractions 540/585,640/590 is 20/69030
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 585,590 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(585,590) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(585,590) x common factors =5 x 1 = 5
LCM(585,590) = ( 585 × 590 ) / 5
LCM(585,590) = 345150 / 5
LCM(585,590) = 69030
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 540,640?
The HCF of 540,640 is 20
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 540/585, 640/590?
Answer: GCF of Numerators as per given numbers 540/585, 640/590 is
GCF of Numerators i.e. for 540,640 is 20
LCM of denominators i.e. for 585,590 is 69030.
Thus, GCF of Fractions is 20/69030.Finally, GCF of Fractions for 540/585, 640/590 is 20/69030.