Use our free GCF of Fractions Calculator tool to compute the GCF of 30/67, 214/21, 962/879 i.e 2/412251 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/67, 214/21, 962/879.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/67,214/21,962/879
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 30/67,214/21,962/879, numerators are 30,214,962
Denominators are 67,21,879
The GCF of 30,214,962 is 2 .
LCM of 67,21,879 is 412251.
The greatest common factor of 30/67,214/21,962/879 = [GCF of 30,214,962]/[LCM of 67,21,879]= 2/412251
Therefore, the GCF of 30/67,214/21,962/879 is 2/412251.
To find the highest common factor of 30,214,962, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 214 are 1, 2, 107, 214
The factors of 962 are 1, 2, 13, 26, 37, 74, 481, 962
The HCF of 30,214,962 is 2.
Lets's calculate GCF of 30,214,962
2 | 30, 214, 962 |
15, 107, 481 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 214
:1,2,107,214
Now, list down the factors of 962
:1,2,13,26,37,74,481,962
Greatest Common Factor
We found the factors 30,214,962 . The biggest common factor number is the GCF number.
So the greatest common factor 30,214,962 is 2.
Lets's calculate LCM of 67,21,879
3 | 67, 21, 879 |
67, 7, 293 |
∴ So the LCM of the given numbers is 3 x 67 x 7 x 293 = 412251
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/412251
Therefore, the GCF of Fractions 30/67,214/21,962/879 is 2/412251
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 67,21,879 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,21,879) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(67,21,879) x common factors =1 x 3 = 3
LCM(67,21,879) = ( 67 × 21 × 879 ) / 3
LCM(67,21,879) = 1236753 / 3
LCM(67,21,879) = 412251
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 30,214,962?
The HCF of 30,214,962 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 30/67, 214/21, 962/879?
Answer: GCF of Numerators as per given numbers 30/67, 214/21, 962/879 is
GCF of Numerators i.e. for 30,214,962 is 2
LCM of denominators i.e. for 67,21,879 is 412251.
Thus, GCF of Fractions is 2/412251.Finally, GCF of Fractions for 30/67, 214/21, 962/879 is 2/412251.