Use our free GCF of Fractions Calculator tool to compute the GCF of 378/420, 434/253 i.e 14/106260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/420, 434/253.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 378/420,434/253
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 378/420,434/253, numerators are 378,434
Denominators are 420,253
The GCF of 378,434 is 14 .
LCM of 420,253 is 106260.
The greatest common factor of 378/420,434/253 = [GCF of 378,434]/[LCM of 420,253]= 14/106260
Therefore, the GCF of 378/420,434/253 is 14/106260.
To find the highest common factor of 378,434, we have to find the factors of both numbers and list the highest common factor.
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The factors of 434 are 1, 2, 7, 14, 31, 62, 217, 434
The HCF of 378,434 is 14.
Lets's calculate GCF of 378,434
2 | 378, 434 |
7 | 189, 217 |
27, 31 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Now, list down the factors of 434
:1,2,7,14,31,62,217,434
Greatest Common Factor
We found the factors 378,434 . The biggest common factor number is the GCF number.
So the greatest common factor 378,434 is 14.
Lets's calculate LCM of 420,253
Given numbers has no common factors except 1. So, there LCM is their product i.e 106260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/106260
Therefore, the GCF of Fractions 378/420,434/253 is 14/106260
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 420,253 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,253) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(420,253) x common factors =1 x 1 = 1
LCM(420,253) = ( 420 × 253 ) / 1
LCM(420,253) = 106260 / 1
LCM(420,253) = 106260
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 378,434?
The HCF of 378,434 is 14
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 378/420, 434/253?
Answer: GCF of Numerators as per given numbers 378/420, 434/253 is
GCF of Numerators i.e. for 378,434 is 14
LCM of denominators i.e. for 420,253 is 106260.
Thus, GCF of Fractions is 14/106260.Finally, GCF of Fractions for 378/420, 434/253 is 14/106260.