Use our free GCF of Fractions Calculator tool to compute the GCF of 274/225, 408/498 i.e 2/37350 easily. The following is the detailed procedure to determine the greatest common factor of fractions 274/225, 408/498.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 274/225,408/498
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 274/225,408/498, numerators are 274,408
Denominators are 225,498
The GCF of 274,408 is 2 .
LCM of 225,498 is 37350.
The greatest common factor of 274/225,408/498 = [GCF of 274,408]/[LCM of 225,498]= 2/37350
Therefore, the GCF of 274/225,408/498 is 2/37350.
To find the highest common factor of 274,408, we have to find the factors of both numbers and list the highest common factor.
The factors of 274 are 1, 2, 137, 274
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The HCF of 274,408 is 2.
Lets's calculate GCF of 274,408
2 | 274, 408 |
137, 204 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 274
:1,2,137,274
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Greatest Common Factor
We found the factors 274,408 . The biggest common factor number is the GCF number.
So the greatest common factor 274,408 is 2.
Lets's calculate LCM of 225,498
3 | 225, 498 |
75, 166 |
∴ So the LCM of the given numbers is 3 x 75 x 166 = 37350
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/37350
Therefore, the GCF of Fractions 274/225,408/498 is 2/37350
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 225,498 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(225,498) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(225,498) x common factors =3 x 1 = 3
LCM(225,498) = ( 225 × 498 ) / 3
LCM(225,498) = 112050 / 3
LCM(225,498) = 37350
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 274,408?
The HCF of 274,408 is 2
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 274/225, 408/498?
Answer: GCF of Numerators as per given numbers 274/225, 408/498 is
GCF of Numerators i.e. for 274,408 is 2
LCM of denominators i.e. for 225,498 is 37350.
Thus, GCF of Fractions is 2/37350.Finally, GCF of Fractions for 274/225, 408/498 is 2/37350.