Use our free GCF of Fractions Calculator tool to compute the GCF of 414/368, 454/667 i.e 2/10672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 414/368, 454/667.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 414/368,454/667
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 414/368,454/667, numerators are 414,454
Denominators are 368,667
The GCF of 414,454 is 2 .
LCM of 368,667 is 10672.
The greatest common factor of 414/368,454/667 = [GCF of 414,454]/[LCM of 368,667]= 2/10672
Therefore, the GCF of 414/368,454/667 is 2/10672.
To find the highest common factor of 414,454, we have to find the factors of both numbers and list the highest common factor.
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The factors of 454 are 1, 2, 227, 454
The HCF of 414,454 is 2.
Lets's calculate GCF of 414,454
2 | 414, 454 |
207, 227 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Now, list down the factors of 454
:1,2,227,454
Greatest Common Factor
We found the factors 414,454 . The biggest common factor number is the GCF number.
So the greatest common factor 414,454 is 2.
Lets's calculate LCM of 368,667
23 | 368, 667 |
16, 29 |
∴ So the LCM of the given numbers is 23 x 16 x 29 = 10672
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/10672
Therefore, the GCF of Fractions 414/368,454/667 is 2/10672
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 368,667 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(368,667) = 23
common factors(in case of two or more numbers have common factors) = 1
GCF(368,667) x common factors =23 x 1 = 23
LCM(368,667) = ( 368 × 667 ) / 23
LCM(368,667) = 245456 / 23
LCM(368,667) = 10672
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 414,454?
The HCF of 414,454 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 414/368, 454/667?
Answer: GCF of Numerators as per given numbers 414/368, 454/667 is
GCF of Numerators i.e. for 414,454 is 2
LCM of denominators i.e. for 368,667 is 10672.
Thus, GCF of Fractions is 2/10672.Finally, GCF of Fractions for 414/368, 454/667 is 2/10672.