Use our free GCF of Fractions Calculator tool to compute the GCF of 216/20, 3000/693 i.e 24/13860 easily. The following is the detailed procedure to determine the greatest common factor of fractions 216/20, 3000/693.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 216/20,3000/693
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 216/20,3000/693, numerators are 216,3000
Denominators are 20,693
The GCF of 216,3000 is 24 .
LCM of 20,693 is 13860.
The greatest common factor of 216/20,3000/693 = [GCF of 216,3000]/[LCM of 20,693]= 24/13860
Therefore, the GCF of 216/20,3000/693 is 24/13860.
To find the highest common factor of 216,3000, we have to find the factors of both numbers and list the highest common factor.
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The factors of 3000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 125, 150, 200, 250, 300, 375, 500, 600, 750, 1000, 1500, 3000
The HCF of 216,3000 is 24.
Lets's calculate GCF of 216,3000
2 | 216, 3000 |
2 | 108, 1500 |
2 | 54, 750 |
3 | 27, 375 |
9, 125 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Now, list down the factors of 3000
:1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,125,150,200,250,300,375,500,600,750,1000,1500,3000
Greatest Common Factor
We found the factors 216,3000 . The biggest common factor number is the GCF number.
So the greatest common factor 216,3000 is 24.
Lets's calculate LCM of 20,693
Given numbers has no common factors except 1. So, there LCM is their product i.e 13860
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/13860
Therefore, the GCF of Fractions 216/20,3000/693 is 24/13860
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 20,693 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,693) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(20,693) x common factors =1 x 1 = 1
LCM(20,693) = ( 20 × 693 ) / 1
LCM(20,693) = 13860 / 1
LCM(20,693) = 13860
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 216,3000?
The HCF of 216,3000 is 24
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 216/20, 3000/693?
Answer: GCF of Numerators as per given numbers 216/20, 3000/693 is
GCF of Numerators i.e. for 216,3000 is 24
LCM of denominators i.e. for 20,693 is 13860.
Thus, GCF of Fractions is 24/13860.Finally, GCF of Fractions for 216/20, 3000/693 is 24/13860.