Use our free GCF of Fractions Calculator tool to compute the GCF of 397/440, 214/768 i.e 1/42240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 397/440, 214/768.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 397/440,214/768
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 397/440,214/768, numerators are 397,214
Denominators are 440,768
The GCF of 397,214 is 1 .
LCM of 440,768 is 42240.
The greatest common factor of 397/440,214/768 = [GCF of 397,214]/[LCM of 440,768]= 1/42240
Therefore, the GCF of 397/440,214/768 is 1/42240.
To find the highest common factor of 397,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 397 are 1, 397
The factors of 214 are 1, 2, 107, 214
The HCF of 397,214 is 1.
Lets's calculate GCF of 397,214
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 397
:1,397
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 397,214 . The biggest common factor number is the GCF number.
So the greatest common factor 397,214 is 1.
Lets's calculate LCM of 440,768
2 | 440, 768 |
2 | 220, 384 |
2 | 110, 192 |
55, 96 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 55 x 96 = 42240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/42240
Therefore, the GCF of Fractions 397/440,214/768 is 1/42240
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 440,768 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(440,768) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(440,768) x common factors =8 x 1 = 8
LCM(440,768) = ( 440 × 768 ) / 8
LCM(440,768) = 337920 / 8
LCM(440,768) = 42240
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 397,214?
The HCF of 397,214 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 397/440, 214/768?
Answer: GCF of Numerators as per given numbers 397/440, 214/768 is
GCF of Numerators i.e. for 397,214 is 1
LCM of denominators i.e. for 440,768 is 42240.
Thus, GCF of Fractions is 1/42240.Finally, GCF of Fractions for 397/440, 214/768 is 1/42240.