Use our free GCF of Fractions Calculator tool to compute the GCF of 516/690, 214/195 i.e 2/8970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 516/690, 214/195.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 516/690,214/195
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 516/690,214/195, numerators are 516,214
Denominators are 690,195
The GCF of 516,214 is 2 .
LCM of 690,195 is 8970.
The greatest common factor of 516/690,214/195 = [GCF of 516,214]/[LCM of 690,195]= 2/8970
Therefore, the GCF of 516/690,214/195 is 2/8970.
To find the highest common factor of 516,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516
The factors of 214 are 1, 2, 107, 214
The HCF of 516,214 is 2.
Lets's calculate GCF of 516,214
2 | 516, 214 |
258, 107 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 516
:1,2,3,4,6,12,43,86,129,172,258,516
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 516,214 . The biggest common factor number is the GCF number.
So the greatest common factor 516,214 is 2.
Lets's calculate LCM of 690,195
3 | 690, 195 |
5 | 230, 65 |
46, 13 |
∴ So the LCM of the given numbers is 3 x 5 x 46 x 13 = 8970
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/8970
Therefore, the GCF of Fractions 516/690,214/195 is 2/8970
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 690,195 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(690,195) = 15
common factors(in case of two or more numbers have common factors) = 1
GCF(690,195) x common factors =15 x 1 = 15
LCM(690,195) = ( 690 × 195 ) / 15
LCM(690,195) = 134550 / 15
LCM(690,195) = 8970
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 516,214?
The HCF of 516,214 is 2
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 516/690, 214/195?
Answer: GCF of Numerators as per given numbers 516/690, 214/195 is
GCF of Numerators i.e. for 516,214 is 2
LCM of denominators i.e. for 690,195 is 8970.
Thus, GCF of Fractions is 2/8970.Finally, GCF of Fractions for 516/690, 214/195 is 2/8970.