Use our free GCF of Fractions Calculator tool to compute the GCF of 40/978, 42/2053 i.e 2/2007834 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/978, 42/2053.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 40/978,42/2053
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 40/978,42/2053, numerators are 40,42
Denominators are 978,2053
The GCF of 40,42 is 2 .
LCM of 978,2053 is 2007834.
The greatest common factor of 40/978,42/2053 = [GCF of 40,42]/[LCM of 978,2053]= 2/2007834
Therefore, the GCF of 40/978,42/2053 is 2/2007834.
To find the highest common factor of 40,42, 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 42 are 1, 2, 3, 6, 7, 14, 21, 42
The HCF of 40,42 is 2.
Lets's calculate GCF of 40,42
2 | 40, 42 |
20, 21 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Greatest Common Factor
We found the factors 40,42 . The biggest common factor number is the GCF number.
So the greatest common factor 40,42 is 2.
Lets's calculate LCM of 978,2053
Given numbers has no common factors except 1. So, there LCM is their product i.e 2007834
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2007834
Therefore, the GCF of Fractions 40/978,42/2053 is 2/2007834
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 978,2053 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(978,2053) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(978,2053) x common factors =1 x 1 = 1
LCM(978,2053) = ( 978 × 2053 ) / 1
LCM(978,2053) = 2007834 / 1
LCM(978,2053) = 2007834
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 40,42?
The HCF of 40,42 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 40/978, 42/2053?
Answer: GCF of Numerators as per given numbers 40/978, 42/2053 is
GCF of Numerators i.e. for 40,42 is 2
LCM of denominators i.e. for 978,2053 is 2007834.
Thus, GCF of Fractions is 2/2007834.Finally, GCF of Fractions for 40/978, 42/2053 is 2/2007834.