Use our free GCF of Fractions Calculator tool to compute the GCF of 213/142, 741/329 i.e 3/46718 easily. The following is the detailed procedure to determine the greatest common factor of fractions 213/142, 741/329.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 213/142,741/329
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 213/142,741/329, numerators are 213,741
Denominators are 142,329
The GCF of 213,741 is 3 .
LCM of 142,329 is 46718.
The greatest common factor of 213/142,741/329 = [GCF of 213,741]/[LCM of 142,329]= 3/46718
Therefore, the GCF of 213/142,741/329 is 3/46718.
To find the highest common factor of 213,741, we have to find the factors of both numbers and list the highest common factor.
The factors of 213 are 1, 3, 71, 213
The factors of 741 are 1, 3, 13, 19, 39, 57, 247, 741
The HCF of 213,741 is 3.
Lets's calculate GCF of 213,741
3 | 213, 741 |
71, 247 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 213
:1,3,71,213
Now, list down the factors of 741
:1,3,13,19,39,57,247,741
Greatest Common Factor
We found the factors 213,741 . The biggest common factor number is the GCF number.
So the greatest common factor 213,741 is 3.
Lets's calculate LCM of 142,329
Given numbers has no common factors except 1. So, there LCM is their product i.e 46718
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/46718
Therefore, the GCF of Fractions 213/142,741/329 is 3/46718
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 142,329 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(142,329) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(142,329) x common factors =1 x 1 = 1
LCM(142,329) = ( 142 × 329 ) / 1
LCM(142,329) = 46718 / 1
LCM(142,329) = 46718
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 213,741?
The HCF of 213,741 is 3
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 213/142, 741/329?
Answer: GCF of Numerators as per given numbers 213/142, 741/329 is
GCF of Numerators i.e. for 213,741 is 3
LCM of denominators i.e. for 142,329 is 46718.
Thus, GCF of Fractions is 3/46718.Finally, GCF of Fractions for 213/142, 741/329 is 3/46718.