Use our free GCF of Fractions Calculator tool to compute the GCF of 417/196, 643/512 i.e 1/25088 easily. The following is the detailed procedure to determine the greatest common factor of fractions 417/196, 643/512.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 417/196,643/512
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 417/196,643/512, numerators are 417,643
Denominators are 196,512
The GCF of 417,643 is 1 .
LCM of 196,512 is 25088.
The greatest common factor of 417/196,643/512 = [GCF of 417,643]/[LCM of 196,512]= 1/25088
Therefore, the GCF of 417/196,643/512 is 1/25088.
To find the highest common factor of 417,643, we have to find the factors of both numbers and list the highest common factor.
The factors of 417 are 1, 3, 139, 417
The factors of 643 are 1, 643
The HCF of 417,643 is 1.
Lets's calculate GCF of 417,643
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 417
:1,3,139,417
Now, list down the factors of 643
:1,643
Greatest Common Factor
We found the factors 417,643 . The biggest common factor number is the GCF number.
So the greatest common factor 417,643 is 1.
Lets's calculate LCM of 196,512
2 | 196, 512 |
2 | 98, 256 |
49, 128 |
∴ So the LCM of the given numbers is 2 x 2 x 49 x 128 = 25088
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/25088
Therefore, the GCF of Fractions 417/196,643/512 is 1/25088
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 196,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(196,512) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(196,512) x common factors =4 x 1 = 4
LCM(196,512) = ( 196 × 512 ) / 4
LCM(196,512) = 100352 / 4
LCM(196,512) = 25088
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 417,643?
The HCF of 417,643 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 417/196, 643/512?
Answer: GCF of Numerators as per given numbers 417/196, 643/512 is
GCF of Numerators i.e. for 417,643 is 1
LCM of denominators i.e. for 196,512 is 25088.
Thus, GCF of Fractions is 1/25088.Finally, GCF of Fractions for 417/196, 643/512 is 1/25088.