Use our free GCF of Fractions Calculator tool to compute the GCF of 105/421, 742/473 i.e 7/199133 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/421, 742/473.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 105/421,742/473
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 105/421,742/473, numerators are 105,742
Denominators are 421,473
The GCF of 105,742 is 7 .
LCM of 421,473 is 199133.
The greatest common factor of 105/421,742/473 = [GCF of 105,742]/[LCM of 421,473]= 7/199133
Therefore, the GCF of 105/421,742/473 is 7/199133.
To find the highest common factor of 105,742, we have to find the factors of both numbers and list the highest common factor.
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The HCF of 105,742 is 7.
Lets's calculate GCF of 105,742
7 | 105, 742 |
15, 106 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Greatest Common Factor
We found the factors 105,742 . The biggest common factor number is the GCF number.
So the greatest common factor 105,742 is 7.
Lets's calculate LCM of 421,473
Given numbers has no common factors except 1. So, there LCM is their product i.e 199133
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/199133
Therefore, the GCF of Fractions 105/421,742/473 is 7/199133
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 421,473 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(421,473) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(421,473) x common factors =1 x 1 = 1
LCM(421,473) = ( 421 × 473 ) / 1
LCM(421,473) = 199133 / 1
LCM(421,473) = 199133
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 105,742?
The HCF of 105,742 is 7
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 105/421, 742/473?
Answer: GCF of Numerators as per given numbers 105/421, 742/473 is
GCF of Numerators i.e. for 105,742 is 7
LCM of denominators i.e. for 421,473 is 199133.
Thus, GCF of Fractions is 7/199133.Finally, GCF of Fractions for 105/421, 742/473 is 7/199133.