Use our free GCF of Fractions Calculator tool to compute the GCF of 338/406, 407/312 i.e 1/63336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 338/406, 407/312.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 338/406,407/312
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 338/406,407/312, numerators are 338,407
Denominators are 406,312
The GCF of 338,407 is 1 .
LCM of 406,312 is 63336.
The greatest common factor of 338/406,407/312 = [GCF of 338,407]/[LCM of 406,312]= 1/63336
Therefore, the GCF of 338/406,407/312 is 1/63336.
To find the highest common factor of 338,407, we have to find the factors of both numbers and list the highest common factor.
The factors of 338 are 1, 2, 13, 26, 169, 338
The factors of 407 are 1, 11, 37, 407
The HCF of 338,407 is 1.
Lets's calculate GCF of 338,407
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 338
:1,2,13,26,169,338
Now, list down the factors of 407
:1,11,37,407
Greatest Common Factor
We found the factors 338,407 . The biggest common factor number is the GCF number.
So the greatest common factor 338,407 is 1.
Lets's calculate LCM of 406,312
2 | 406, 312 |
203, 156 |
∴ So the LCM of the given numbers is 2 x 203 x 156 = 63336
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/63336
Therefore, the GCF of Fractions 338/406,407/312 is 1/63336
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 406,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,312) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(406,312) x common factors =2 x 1 = 2
LCM(406,312) = ( 406 × 312 ) / 2
LCM(406,312) = 126672 / 2
LCM(406,312) = 63336
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 338,407?
The HCF of 338,407 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 338/406, 407/312?
Answer: GCF of Numerators as per given numbers 338/406, 407/312 is
GCF of Numerators i.e. for 338,407 is 1
LCM of denominators i.e. for 406,312 is 63336.
Thus, GCF of Fractions is 1/63336.Finally, GCF of Fractions for 338/406, 407/312 is 1/63336.