Use our free GCF of Fractions Calculator tool to compute the GCF of 216/500, 849/620 i.e 3/15500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 216/500, 849/620.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 216/500,849/620
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 216/500,849/620, numerators are 216,849
Denominators are 500,620
The GCF of 216,849 is 3 .
LCM of 500,620 is 15500.
The greatest common factor of 216/500,849/620 = [GCF of 216,849]/[LCM of 500,620]= 3/15500
Therefore, the GCF of 216/500,849/620 is 3/15500.
To find the highest common factor of 216,849, 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 849 are 1, 3, 283, 849
The HCF of 216,849 is 3.
Lets's calculate GCF of 216,849
3 | 216, 849 |
72, 283 |
∴ So the GCF of the given numbers is 3 = 3
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 849
:1,3,283,849
Greatest Common Factor
We found the factors 216,849 . The biggest common factor number is the GCF number.
So the greatest common factor 216,849 is 3.
Lets's calculate LCM of 500,620
2 | 500, 620 |
2 | 250, 310 |
5 | 125, 155 |
25, 31 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 25 x 31 = 15500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/15500
Therefore, the GCF of Fractions 216/500,849/620 is 3/15500
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 500,620 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(500,620) = 20
common factors(in case of two or more numbers have common factors) = 1
GCF(500,620) x common factors =20 x 1 = 20
LCM(500,620) = ( 500 × 620 ) / 20
LCM(500,620) = 310000 / 20
LCM(500,620) = 15500
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 216,849?
The HCF of 216,849 is 3
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 216/500, 849/620?
Answer: GCF of Numerators as per given numbers 216/500, 849/620 is
GCF of Numerators i.e. for 216,849 is 3
LCM of denominators i.e. for 500,620 is 15500.
Thus, GCF of Fractions is 3/15500.Finally, GCF of Fractions for 216/500, 849/620 is 3/15500.