Use our free GCF of Fractions Calculator tool to compute the GCF of 721/768, 410/384 i.e 1/768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 721/768, 410/384.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 721/768,410/384
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 721/768,410/384, numerators are 721,410
Denominators are 768,384
The GCF of 721,410 is 1 .
LCM of 768,384 is 768.
The greatest common factor of 721/768,410/384 = [GCF of 721,410]/[LCM of 768,384]= 1/768
Therefore, the GCF of 721/768,410/384 is 1/768.
To find the highest common factor of 721,410, we have to find the factors of both numbers and list the highest common factor.
The factors of 721 are 1, 7, 103, 721
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The HCF of 721,410 is 1.
Lets's calculate GCF of 721,410
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 721
:1,7,103,721
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Greatest Common Factor
We found the factors 721,410 . The biggest common factor number is the GCF number.
So the greatest common factor 721,410 is 1.
Lets's calculate LCM of 768,384
2 | 768, 384 |
2 | 384, 192 |
2 | 96, 192 |
2 | 48, 96 |
2 | 24, 48 |
2 | 12, 24 |
2 | 6, 12 |
3 | 3, 6 |
1, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 1 x 2 = 768
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/768
Therefore, the GCF of Fractions 721/768,410/384 is 1/768
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 768,384 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(768,384) = 384
common factors(in case of two or more numbers have common factors) = 1
GCF(768,384) x common factors =384 x 1 = 384
LCM(768,384) = ( 768 × 384 ) / 384
LCM(768,384) = 294912 / 384
LCM(768,384) = 768
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 721,410?
The HCF of 721,410 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 721/768, 410/384?
Answer: GCF of Numerators as per given numbers 721/768, 410/384 is
GCF of Numerators i.e. for 721,410 is 1
LCM of denominators i.e. for 768,384 is 768.
Thus, GCF of Fractions is 1/768.Finally, GCF of Fractions for 721/768, 410/384 is 1/768.