Use our free GCF of Fractions Calculator tool to compute the GCF of 101/412, 400/742 i.e 1/152852 easily. The following is the detailed procedure to determine the greatest common factor of fractions 101/412, 400/742.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 101/412,400/742
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 101/412,400/742, numerators are 101,400
Denominators are 412,742
The GCF of 101,400 is 1 .
LCM of 412,742 is 152852.
The greatest common factor of 101/412,400/742 = [GCF of 101,400]/[LCM of 412,742]= 1/152852
Therefore, the GCF of 101/412,400/742 is 1/152852.
To find the highest common factor of 101,400, we have to find the factors of both numbers and list the highest common factor.
The factors of 101 are 1, 101
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The HCF of 101,400 is 1.
Lets's calculate GCF of 101,400
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 101
:1,101
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 101,400 . The biggest common factor number is the GCF number.
So the greatest common factor 101,400 is 1.
Lets's calculate LCM of 412,742
2 | 412, 742 |
206, 371 |
∴ So the LCM of the given numbers is 2 x 206 x 371 = 152852
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/152852
Therefore, the GCF of Fractions 101/412,400/742 is 1/152852
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 412,742 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(412,742) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(412,742) x common factors =2 x 1 = 2
LCM(412,742) = ( 412 × 742 ) / 2
LCM(412,742) = 305704 / 2
LCM(412,742) = 152852
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 101,400?
The HCF of 101,400 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 101/412, 400/742?
Answer: GCF of Numerators as per given numbers 101/412, 400/742 is
GCF of Numerators i.e. for 101,400 is 1
LCM of denominators i.e. for 412,742 is 152852.
Thus, GCF of Fractions is 1/152852.Finally, GCF of Fractions for 101/412, 400/742 is 1/152852.