Use our free GCF of Fractions Calculator tool to compute the GCF of 35/523, 38/897, 214/845 i.e 1/30493515 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/523, 38/897, 214/845.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 35/523,38/897,214/845
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 35/523,38/897,214/845, numerators are 35,38,214
Denominators are 523,897,845
The GCF of 35,38,214 is 1 .
LCM of 523,897,845 is 30493515.
The greatest common factor of 35/523,38/897,214/845 = [GCF of 35,38,214]/[LCM of 523,897,845]= 1/30493515
Therefore, the GCF of 35/523,38/897,214/845 is 1/30493515.
To find the highest common factor of 35,38,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 35 are 1, 5, 7, 35
The factors of 38 are 1, 2, 19, 38
The factors of 214 are 1, 2, 107, 214
The HCF of 35,38,214 is 1.
Lets's calculate GCF of 35,38,214
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 35,38,214 . The biggest common factor number is the GCF number.
So the greatest common factor 35,38,214 is 1.
Lets's calculate LCM of 523,897,845
13 | 523, 897, 845 |
523, 69, 65 |
∴ So the LCM of the given numbers is 13 x 523 x 69 x 65 = 30493515
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30493515
Therefore, the GCF of Fractions 35/523,38/897,214/845 is 1/30493515
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 523,897,845 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(523,897,845) = 1
common factors(in case of two or more numbers have common factors) = 13
GCF(523,897,845) x common factors =1 x 13 = 13
LCM(523,897,845) = ( 523 × 897 × 845 ) / 13
LCM(523,897,845) = 396415695 / 13
LCM(523,897,845) = 30493515
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 35,38,214?
The HCF of 35,38,214 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 35/523, 38/897, 214/845?
Answer: GCF of Numerators as per given numbers 35/523, 38/897, 214/845 is
GCF of Numerators i.e. for 35,38,214 is 1
LCM of denominators i.e. for 523,897,845 is 30493515.
Thus, GCF of Fractions is 1/30493515.Finally, GCF of Fractions for 35/523, 38/897, 214/845 is 1/30493515.