Use our free GCF of Fractions Calculator tool to compute the GCF of 374/454, 419/318 i.e 1/72186 easily. The following is the detailed procedure to determine the greatest common factor of fractions 374/454, 419/318.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 374/454,419/318
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 374/454,419/318, numerators are 374,419
Denominators are 454,318
The GCF of 374,419 is 1 .
LCM of 454,318 is 72186.
The greatest common factor of 374/454,419/318 = [GCF of 374,419]/[LCM of 454,318]= 1/72186
Therefore, the GCF of 374/454,419/318 is 1/72186.
To find the highest common factor of 374,419, we have to find the factors of both numbers and list the highest common factor.
The factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374
The factors of 419 are 1, 419
The HCF of 374,419 is 1.
Lets's calculate GCF of 374,419
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 374
:1,2,11,17,22,34,187,374
Now, list down the factors of 419
:1,419
Greatest Common Factor
We found the factors 374,419 . The biggest common factor number is the GCF number.
So the greatest common factor 374,419 is 1.
Lets's calculate LCM of 454,318
2 | 454, 318 |
227, 159 |
∴ So the LCM of the given numbers is 2 x 227 x 159 = 72186
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/72186
Therefore, the GCF of Fractions 374/454,419/318 is 1/72186
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 454,318 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(454,318) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(454,318) x common factors =2 x 1 = 2
LCM(454,318) = ( 454 × 318 ) / 2
LCM(454,318) = 144372 / 2
LCM(454,318) = 72186
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 374,419?
The HCF of 374,419 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 374/454, 419/318?
Answer: GCF of Numerators as per given numbers 374/454, 419/318 is
GCF of Numerators i.e. for 374,419 is 1
LCM of denominators i.e. for 454,318 is 72186.
Thus, GCF of Fractions is 1/72186.Finally, GCF of Fractions for 374/454, 419/318 is 1/72186.