Use our free GCF of Fractions Calculator tool to compute the GCF of 399/214, 216/910 i.e 3/97370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 399/214, 216/910.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 399/214,216/910
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 399/214,216/910, numerators are 399,216
Denominators are 214,910
The GCF of 399,216 is 3 .
LCM of 214,910 is 97370.
The greatest common factor of 399/214,216/910 = [GCF of 399,216]/[LCM of 214,910]= 3/97370
Therefore, the GCF of 399/214,216/910 is 3/97370.
To find the highest common factor of 399,216, we have to find the factors of both numbers and list the highest common factor.
The factors of 399 are 1, 3, 7, 19, 21, 57, 133, 399
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The HCF of 399,216 is 3.
Lets's calculate GCF of 399,216
3 | 399, 216 |
133, 72 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 399
:1,3,7,19,21,57,133,399
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Greatest Common Factor
We found the factors 399,216 . The biggest common factor number is the GCF number.
So the greatest common factor 399,216 is 3.
Lets's calculate LCM of 214,910
2 | 214, 910 |
107, 455 |
∴ So the LCM of the given numbers is 2 x 107 x 455 = 97370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/97370
Therefore, the GCF of Fractions 399/214,216/910 is 3/97370
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 214,910 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,910) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(214,910) x common factors =2 x 1 = 2
LCM(214,910) = ( 214 × 910 ) / 2
LCM(214,910) = 194740 / 2
LCM(214,910) = 97370
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 399,216?
The HCF of 399,216 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 399/214, 216/910?
Answer: GCF of Numerators as per given numbers 399/214, 216/910 is
GCF of Numerators i.e. for 399,216 is 3
LCM of denominators i.e. for 214,910 is 97370.
Thus, GCF of Fractions is 3/97370.Finally, GCF of Fractions for 399/214, 216/910 is 3/97370.