Use our free GCF of Fractions Calculator tool to compute the GCF of 414/532, 109/296 i.e 1/39368 easily. The following is the detailed procedure to determine the greatest common factor of fractions 414/532, 109/296.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 414/532,109/296
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 414/532,109/296, numerators are 414,109
Denominators are 532,296
The GCF of 414,109 is 1 .
LCM of 532,296 is 39368.
The greatest common factor of 414/532,109/296 = [GCF of 414,109]/[LCM of 532,296]= 1/39368
Therefore, the GCF of 414/532,109/296 is 1/39368.
To find the highest common factor of 414,109, we have to find the factors of both numbers and list the highest common factor.
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The factors of 109 are 1, 109
The HCF of 414,109 is 1.
Lets's calculate GCF of 414,109
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Now, list down the factors of 109
:1,109
Greatest Common Factor
We found the factors 414,109 . The biggest common factor number is the GCF number.
So the greatest common factor 414,109 is 1.
Lets's calculate LCM of 532,296
2 | 532, 296 |
2 | 266, 148 |
133, 74 |
∴ So the LCM of the given numbers is 2 x 2 x 133 x 74 = 39368
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/39368
Therefore, the GCF of Fractions 414/532,109/296 is 1/39368
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 532,296 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(532,296) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(532,296) x common factors =4 x 1 = 4
LCM(532,296) = ( 532 × 296 ) / 4
LCM(532,296) = 157472 / 4
LCM(532,296) = 39368
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 414,109?
The HCF of 414,109 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 414/532, 109/296?
Answer: GCF of Numerators as per given numbers 414/532, 109/296 is
GCF of Numerators i.e. for 414,109 is 1
LCM of denominators i.e. for 532,296 is 39368.
Thus, GCF of Fractions is 1/39368.Finally, GCF of Fractions for 414/532, 109/296 is 1/39368.