Use our free GCF of Fractions Calculator tool to compute the GCF of 376/419, 294/414 i.e 2/173466 easily. The following is the detailed procedure to determine the greatest common factor of fractions 376/419, 294/414.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 376/419,294/414
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 376/419,294/414, numerators are 376,294
Denominators are 419,414
The GCF of 376,294 is 2 .
LCM of 419,414 is 173466.
The greatest common factor of 376/419,294/414 = [GCF of 376,294]/[LCM of 419,414]= 2/173466
Therefore, the GCF of 376/419,294/414 is 2/173466.
To find the highest common factor of 376,294, we have to find the factors of both numbers and list the highest common factor.
The factors of 376 are 1, 2, 4, 8, 47, 94, 188, 376
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The HCF of 376,294 is 2.
Lets's calculate GCF of 376,294
2 | 376, 294 |
188, 147 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 376
:1,2,4,8,47,94,188,376
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Greatest Common Factor
We found the factors 376,294 . The biggest common factor number is the GCF number.
So the greatest common factor 376,294 is 2.
Lets's calculate LCM of 419,414
Given numbers has no common factors except 1. So, there LCM is their product i.e 173466
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/173466
Therefore, the GCF of Fractions 376/419,294/414 is 2/173466
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 419,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(419,414) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(419,414) x common factors =1 x 1 = 1
LCM(419,414) = ( 419 × 414 ) / 1
LCM(419,414) = 173466 / 1
LCM(419,414) = 173466
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 376,294?
The HCF of 376,294 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 376/419, 294/414?
Answer: GCF of Numerators as per given numbers 376/419, 294/414 is
GCF of Numerators i.e. for 376,294 is 2
LCM of denominators i.e. for 419,414 is 173466.
Thus, GCF of Fractions is 2/173466.Finally, GCF of Fractions for 376/419, 294/414 is 2/173466.