Use our free GCF of Fractions Calculator tool to compute the GCF of 37/69, 398/42, 407/498 i.e 1/80178 easily. The following is the detailed procedure to determine the greatest common factor of fractions 37/69, 398/42, 407/498.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 37/69,398/42,407/498
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 37/69,398/42,407/498, numerators are 37,398,407
Denominators are 69,42,498
The GCF of 37,398,407 is 1 .
LCM of 69,42,498 is 80178.
The greatest common factor of 37/69,398/42,407/498 = [GCF of 37,398,407]/[LCM of 69,42,498]= 1/80178
Therefore, the GCF of 37/69,398/42,407/498 is 1/80178.
To find the highest common factor of 37,398,407, we have to find the factors of both numbers and list the highest common factor.
The factors of 37 are 1, 37
The factors of 398 are 1, 2, 199, 398
The factors of 407 are 1, 11, 37, 407
The HCF of 37,398,407 is 1.
Lets's calculate GCF of 37,398,407
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 37
:1,37
Now, list down the factors of 398
:1,2,199,398
Now, list down the factors of 407
:1,11,37,407
Greatest Common Factor
We found the factors 37,398,407 . The biggest common factor number is the GCF number.
So the greatest common factor 37,398,407 is 1.
Lets's calculate LCM of 69,42,498
2 | 69, 42, 498 |
3 | 69, 21, 249 |
23, 7, 83 |
∴ So the LCM of the given numbers is 2 x 3 x 23 x 7 x 83 = 80178
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/80178
Therefore, the GCF of Fractions 37/69,398/42,407/498 is 1/80178
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 69,42,498 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,42,498) = 3
common factors(in case of two or more numbers have common factors) = 6
GCF(69,42,498) x common factors =3 x 6 = 18
LCM(69,42,498) = ( 69 × 42 × 498 ) / 18
LCM(69,42,498) = 1443204 / 18
LCM(69,42,498) = 80178
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 37,398,407?
The HCF of 37,398,407 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 37/69, 398/42, 407/498?
Answer: GCF of Numerators as per given numbers 37/69, 398/42, 407/498 is
GCF of Numerators i.e. for 37,398,407 is 1
LCM of denominators i.e. for 69,42,498 is 80178.
Thus, GCF of Fractions is 1/80178.Finally, GCF of Fractions for 37/69, 398/42, 407/498 is 1/80178.