Use our free GCF of Fractions Calculator tool to compute the GCF of 30/96, 164/20, 321/126 i.e 1/10080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/96, 164/20, 321/126.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/96,164/20,321/126
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 30/96,164/20,321/126, numerators are 30,164,321
Denominators are 96,20,126
The GCF of 30,164,321 is 1 .
LCM of 96,20,126 is 10080.
The greatest common factor of 30/96,164/20,321/126 = [GCF of 30,164,321]/[LCM of 96,20,126]= 1/10080
Therefore, the GCF of 30/96,164/20,321/126 is 1/10080.
To find the highest common factor of 30,164,321, 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 164 are 1, 2, 4, 41, 82, 164
The factors of 321 are 1, 3, 107, 321
The HCF of 30,164,321 is 1.
Lets's calculate GCF of 30,164,321
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 164
:1,2,4,41,82,164
Now, list down the factors of 321
:1,3,107,321
Greatest Common Factor
We found the factors 30,164,321 . The biggest common factor number is the GCF number.
So the greatest common factor 30,164,321 is 1.
Lets's calculate LCM of 96,20,126
2 | 96, 20, 126 |
2 | 48, 10, 63 |
3 | 24, 5, 63 |
8, 5, 21 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 8 x 5 x 21 = 10080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10080
Therefore, the GCF of Fractions 30/96,164/20,321/126 is 1/10080
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 96,20,126 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,20,126) = 2
common factors(in case of two or more numbers have common factors) = 12
GCF(96,20,126) x common factors =2 x 12 = 24
LCM(96,20,126) = ( 96 × 20 × 126 ) / 24
LCM(96,20,126) = 241920 / 24
LCM(96,20,126) = 10080
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 30,164,321?
The HCF of 30,164,321 is 1
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 30/96, 164/20, 321/126?
Answer: GCF of Numerators as per given numbers 30/96, 164/20, 321/126 is
GCF of Numerators i.e. for 30,164,321 is 1
LCM of denominators i.e. for 96,20,126 is 10080.
Thus, GCF of Fractions is 1/10080.Finally, GCF of Fractions for 30/96, 164/20, 321/126 is 1/10080.