Use our free GCF of Fractions Calculator tool to compute the GCF of 454/919, 406/678 i.e 2/623082 easily. The following is the detailed procedure to determine the greatest common factor of fractions 454/919, 406/678.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 454/919,406/678
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 454/919,406/678, numerators are 454,406
Denominators are 919,678
The GCF of 454,406 is 2 .
LCM of 919,678 is 623082.
The greatest common factor of 454/919,406/678 = [GCF of 454,406]/[LCM of 919,678]= 2/623082
Therefore, the GCF of 454/919,406/678 is 2/623082.
To find the highest common factor of 454,406, we have to find the factors of both numbers and list the highest common factor.
The factors of 454 are 1, 2, 227, 454
The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406
The HCF of 454,406 is 2.
Lets's calculate GCF of 454,406
2 | 454, 406 |
227, 203 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 454
:1,2,227,454
Now, list down the factors of 406
:1,2,7,14,29,58,203,406
Greatest Common Factor
We found the factors 454,406 . The biggest common factor number is the GCF number.
So the greatest common factor 454,406 is 2.
Lets's calculate LCM of 919,678
Given numbers has no common factors except 1. So, there LCM is their product i.e 623082
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/623082
Therefore, the GCF of Fractions 454/919,406/678 is 2/623082
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 919,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(919,678) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(919,678) x common factors =1 x 1 = 1
LCM(919,678) = ( 919 × 678 ) / 1
LCM(919,678) = 623082 / 1
LCM(919,678) = 623082
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 454,406?
The HCF of 454,406 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 454/919, 406/678?
Answer: GCF of Numerators as per given numbers 454/919, 406/678 is
GCF of Numerators i.e. for 454,406 is 2
LCM of denominators i.e. for 919,678 is 623082.
Thus, GCF of Fractions is 2/623082.Finally, GCF of Fractions for 454/919, 406/678 is 2/623082.