Use our free GCF of Fractions Calculator tool to compute the GCF of 38/309, 421/486, 514/428 i.e 1/10712412 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/309, 421/486, 514/428.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 38/309,421/486,514/428
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 38/309,421/486,514/428, numerators are 38,421,514
Denominators are 309,486,428
The GCF of 38,421,514 is 1 .
LCM of 309,486,428 is 10712412.
The greatest common factor of 38/309,421/486,514/428 = [GCF of 38,421,514]/[LCM of 309,486,428]= 1/10712412
Therefore, the GCF of 38/309,421/486,514/428 is 1/10712412.
To find the highest common factor of 38,421,514, we have to find the factors of both numbers and list the highest common factor.
The factors of 38 are 1, 2, 19, 38
The factors of 421 are 1, 421
The factors of 514 are 1, 2, 257, 514
The HCF of 38,421,514 is 1.
Lets's calculate GCF of 38,421,514
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 421
:1,421
Now, list down the factors of 514
:1,2,257,514
Greatest Common Factor
We found the factors 38,421,514 . The biggest common factor number is the GCF number.
So the greatest common factor 38,421,514 is 1.
Lets's calculate LCM of 309,486,428
2 | 309, 486, 428 |
3 | 309, 243, 214 |
103, 81, 214 |
∴ So the LCM of the given numbers is 2 x 3 x 103 x 81 x 214 = 10712412
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10712412
Therefore, the GCF of Fractions 38/309,421/486,514/428 is 1/10712412
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 309,486,428 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,486,428) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(309,486,428) x common factors =1 x 6 = 6
LCM(309,486,428) = ( 309 × 486 × 428 ) / 6
LCM(309,486,428) = 64274472 / 6
LCM(309,486,428) = 10712412
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 38,421,514?
The HCF of 38,421,514 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 38/309, 421/486, 514/428?
Answer: GCF of Numerators as per given numbers 38/309, 421/486, 514/428 is
GCF of Numerators i.e. for 38,421,514 is 1
LCM of denominators i.e. for 309,486,428 is 10712412.
Thus, GCF of Fractions is 1/10712412.Finally, GCF of Fractions for 38/309, 421/486, 514/428 is 1/10712412.