Use our free GCF of Fractions Calculator tool to compute the GCF of 738/420, 6354/339 i.e 18/47460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 738/420, 6354/339.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 738/420,6354/339
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 738/420,6354/339, numerators are 738,6354
Denominators are 420,339
The GCF of 738,6354 is 18 .
LCM of 420,339 is 47460.
The greatest common factor of 738/420,6354/339 = [GCF of 738,6354]/[LCM of 420,339]= 18/47460
Therefore, the GCF of 738/420,6354/339 is 18/47460.
To find the highest common factor of 738,6354, we have to find the factors of both numbers and list the highest common factor.
The factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738
The factors of 6354 are 1, 2, 3, 6, 9, 18, 353, 706, 1059, 2118, 3177, 6354
The HCF of 738,6354 is 18.
Lets's calculate GCF of 738,6354
2 | 738, 6354 |
3 | 369, 3177 |
3 | 123, 1059 |
41, 353 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Now, list down the factors of 738
:1,2,3,6,9,18,41,82,123,246,369,738
Now, list down the factors of 6354
:1,2,3,6,9,18,353,706,1059,2118,3177,6354
Greatest Common Factor
We found the factors 738,6354 . The biggest common factor number is the GCF number.
So the greatest common factor 738,6354 is 18.
Lets's calculate LCM of 420,339
3 | 420, 339 |
140, 113 |
∴ So the LCM of the given numbers is 3 x 140 x 113 = 47460
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/47460
Therefore, the GCF of Fractions 738/420,6354/339 is 18/47460
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 420,339 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,339) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(420,339) x common factors =3 x 1 = 3
LCM(420,339) = ( 420 × 339 ) / 3
LCM(420,339) = 142380 / 3
LCM(420,339) = 47460
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 738,6354?
The HCF of 738,6354 is 18
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 738/420, 6354/339?
Answer: GCF of Numerators as per given numbers 738/420, 6354/339 is
GCF of Numerators i.e. for 738,6354 is 18
LCM of denominators i.e. for 420,339 is 47460.
Thus, GCF of Fractions is 18/47460.Finally, GCF of Fractions for 738/420, 6354/339 is 18/47460.