Use our free GCF of Fractions Calculator tool to compute the GCF of 30/53, 289/30, 210/312 i.e 1/82680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/53, 289/30, 210/312.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/53,289/30,210/312
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 30/53,289/30,210/312, numerators are 30,289,210
Denominators are 53,30,312
The GCF of 30,289,210 is 1 .
LCM of 53,30,312 is 82680.
The greatest common factor of 30/53,289/30,210/312 = [GCF of 30,289,210]/[LCM of 53,30,312]= 1/82680
Therefore, the GCF of 30/53,289/30,210/312 is 1/82680.
To find the highest common factor of 30,289,210, 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 289 are 1, 17, 289
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 30,289,210 is 1.
Lets's calculate GCF of 30,289,210
∴ 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 289
:1,17,289
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 30,289,210 . The biggest common factor number is the GCF number.
So the greatest common factor 30,289,210 is 1.
Lets's calculate LCM of 53,30,312
2 | 53, 30, 312 |
3 | 53, 15, 156 |
53, 5, 52 |
∴ So the LCM of the given numbers is 2 x 3 x 53 x 5 x 52 = 82680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/82680
Therefore, the GCF of Fractions 30/53,289/30,210/312 is 1/82680
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 53,30,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(53,30,312) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(53,30,312) x common factors =1 x 6 = 6
LCM(53,30,312) = ( 53 × 30 × 312 ) / 6
LCM(53,30,312) = 496080 / 6
LCM(53,30,312) = 82680
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 30,289,210?
The HCF of 30,289,210 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 30/53, 289/30, 210/312?
Answer: GCF of Numerators as per given numbers 30/53, 289/30, 210/312 is
GCF of Numerators i.e. for 30,289,210 is 1
LCM of denominators i.e. for 53,30,312 is 82680.
Thus, GCF of Fractions is 1/82680.Finally, GCF of Fractions for 30/53, 289/30, 210/312 is 1/82680.