Use our free GCF of Fractions Calculator tool to compute the GCF of 402/320, 249/960 i.e 3/960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 402/320, 249/960.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 402/320,249/960
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 402/320,249/960, numerators are 402,249
Denominators are 320,960
The GCF of 402,249 is 3 .
LCM of 320,960 is 960.
The greatest common factor of 402/320,249/960 = [GCF of 402,249]/[LCM of 320,960]= 3/960
Therefore, the GCF of 402/320,249/960 is 3/960.
To find the highest common factor of 402,249, we have to find the factors of both numbers and list the highest common factor.
The factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402
The factors of 249 are 1, 3, 83, 249
The HCF of 402,249 is 3.
Lets's calculate GCF of 402,249
3 | 402, 249 |
134, 83 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 402
:1,2,3,6,67,134,201,402
Now, list down the factors of 249
:1,3,83,249
Greatest Common Factor
We found the factors 402,249 . The biggest common factor number is the GCF number.
So the greatest common factor 402,249 is 3.
Lets's calculate LCM of 320,960
2 | 320, 960 |
2 | 160, 480 |
2 | 80, 240 |
2 | 40, 120 |
2 | 20, 60 |
2 | 10, 30 |
5 | 5, 15 |
1, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 5 x 1 x 3 = 960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/960
Therefore, the GCF of Fractions 402/320,249/960 is 3/960
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 320,960 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,960) = 320
common factors(in case of two or more numbers have common factors) = 1
GCF(320,960) x common factors =320 x 1 = 320
LCM(320,960) = ( 320 × 960 ) / 320
LCM(320,960) = 307200 / 320
LCM(320,960) = 960
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 402,249?
The HCF of 402,249 is 3
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 402/320, 249/960?
Answer: GCF of Numerators as per given numbers 402/320, 249/960 is
GCF of Numerators i.e. for 402,249 is 3
LCM of denominators i.e. for 320,960 is 960.
Thus, GCF of Fractions is 3/960.Finally, GCF of Fractions for 402/320, 249/960 is 3/960.