Use our free GCF of Fractions Calculator tool to compute the GCF of 40/56, 997/21, 108/300 i.e 1/4200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/56, 997/21, 108/300.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 40/56,997/21,108/300
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 40/56,997/21,108/300, numerators are 40,997,108
Denominators are 56,21,300
The GCF of 40,997,108 is 1 .
LCM of 56,21,300 is 4200.
The greatest common factor of 40/56,997/21,108/300 = [GCF of 40,997,108]/[LCM of 56,21,300]= 1/4200
Therefore, the GCF of 40/56,997/21,108/300 is 1/4200.
To find the highest common factor of 40,997,108, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 997 are 1, 997
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The HCF of 40,997,108 is 1.
Lets's calculate GCF of 40,997,108
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 997
:1,997
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Greatest Common Factor
We found the factors 40,997,108 . The biggest common factor number is the GCF number.
So the greatest common factor 40,997,108 is 1.
Lets's calculate LCM of 56,21,300
2 | 56, 21, 300 |
2 | 28, 21, 150 |
3 | 14, 21, 75 |
7 | 14, 7, 25 |
2, 1, 25 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 2 x 1 x 25 = 4200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4200
Therefore, the GCF of Fractions 40/56,997/21,108/300 is 1/4200
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 56,21,300 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(56,21,300) = 1
common factors(in case of two or more numbers have common factors) = 84
GCF(56,21,300) x common factors =1 x 84 = 84
LCM(56,21,300) = ( 56 × 21 × 300 ) / 84
LCM(56,21,300) = 352800 / 84
LCM(56,21,300) = 4200
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 40,997,108?
The HCF of 40,997,108 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 40/56, 997/21, 108/300?
Answer: GCF of Numerators as per given numbers 40/56, 997/21, 108/300 is
GCF of Numerators i.e. for 40,997,108 is 1
LCM of denominators i.e. for 56,21,300 is 4200.
Thus, GCF of Fractions is 1/4200.Finally, GCF of Fractions for 40/56, 997/21, 108/300 is 1/4200.