Use our free GCF of Fractions Calculator tool to compute the GCF of 146/105, 343/448 i.e 1/6720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 146/105, 343/448.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 146/105,343/448
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 146/105,343/448, numerators are 146,343
Denominators are 105,448
The GCF of 146,343 is 1 .
LCM of 105,448 is 6720.
The greatest common factor of 146/105,343/448 = [GCF of 146,343]/[LCM of 105,448]= 1/6720
Therefore, the GCF of 146/105,343/448 is 1/6720.
To find the highest common factor of 146,343, we have to find the factors of both numbers and list the highest common factor.
The factors of 146 are 1, 2, 73, 146
The factors of 343 are 1, 7, 49, 343
The HCF of 146,343 is 1.
Lets's calculate GCF of 146,343
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 146
:1,2,73,146
Now, list down the factors of 343
:1,7,49,343
Greatest Common Factor
We found the factors 146,343 . The biggest common factor number is the GCF number.
So the greatest common factor 146,343 is 1.
Lets's calculate LCM of 105,448
7 | 105, 448 |
15, 64 |
∴ So the LCM of the given numbers is 7 x 15 x 64 = 6720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6720
Therefore, the GCF of Fractions 146/105,343/448 is 1/6720
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 105,448 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,448) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(105,448) x common factors =7 x 1 = 7
LCM(105,448) = ( 105 × 448 ) / 7
LCM(105,448) = 47040 / 7
LCM(105,448) = 6720
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 146,343?
The HCF of 146,343 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 146/105, 343/448?
Answer: GCF of Numerators as per given numbers 146/105, 343/448 is
GCF of Numerators i.e. for 146,343 is 1
LCM of denominators i.e. for 105,448 is 6720.
Thus, GCF of Fractions is 1/6720.Finally, GCF of Fractions for 146/105, 343/448 is 1/6720.