Use our free GCF of Fractions Calculator tool to compute the GCF of 45/28, 212/54, 619/208 i.e 1/39312 easily. The following is the detailed procedure to determine the greatest common factor of fractions 45/28, 212/54, 619/208.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 45/28,212/54,619/208
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 45/28,212/54,619/208, numerators are 45,212,619
Denominators are 28,54,208
The GCF of 45,212,619 is 1 .
LCM of 28,54,208 is 39312.
The greatest common factor of 45/28,212/54,619/208 = [GCF of 45,212,619]/[LCM of 28,54,208]= 1/39312
Therefore, the GCF of 45/28,212/54,619/208 is 1/39312.
To find the highest common factor of 45,212,619, we have to find the factors of both numbers and list the highest common factor.
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 212 are 1, 2, 4, 53, 106, 212
The factors of 619 are 1, 619
The HCF of 45,212,619 is 1.
Lets's calculate GCF of 45,212,619
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 212
:1,2,4,53,106,212
Now, list down the factors of 619
:1,619
Greatest Common Factor
We found the factors 45,212,619 . The biggest common factor number is the GCF number.
So the greatest common factor 45,212,619 is 1.
Lets's calculate LCM of 28,54,208
2 | 28, 54, 208 |
2 | 14, 27, 104 |
7, 27, 52 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 27 x 52 = 39312
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/39312
Therefore, the GCF of Fractions 45/28,212/54,619/208 is 1/39312
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 28,54,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,54,208) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(28,54,208) x common factors =2 x 4 = 8
LCM(28,54,208) = ( 28 × 54 × 208 ) / 8
LCM(28,54,208) = 314496 / 8
LCM(28,54,208) = 39312
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 45,212,619?
The HCF of 45,212,619 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 45/28, 212/54, 619/208?
Answer: GCF of Numerators as per given numbers 45/28, 212/54, 619/208 is
GCF of Numerators i.e. for 45,212,619 is 1
LCM of denominators i.e. for 28,54,208 is 39312.
Thus, GCF of Fractions is 1/39312.Finally, GCF of Fractions for 45/28, 212/54, 619/208 is 1/39312.