Use our free GCF of Fractions Calculator tool to compute the GCF of 269/402, 768/912 i.e 1/61104 easily. The following is the detailed procedure to determine the greatest common factor of fractions 269/402, 768/912.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 269/402,768/912
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 269/402,768/912, numerators are 269,768
Denominators are 402,912
The GCF of 269,768 is 1 .
LCM of 402,912 is 61104.
The greatest common factor of 269/402,768/912 = [GCF of 269,768]/[LCM of 402,912]= 1/61104
Therefore, the GCF of 269/402,768/912 is 1/61104.
To find the highest common factor of 269,768, we have to find the factors of both numbers and list the highest common factor.
The factors of 269 are 1, 269
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The HCF of 269,768 is 1.
Lets's calculate GCF of 269,768
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 269
:1,269
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Greatest Common Factor
We found the factors 269,768 . The biggest common factor number is the GCF number.
So the greatest common factor 269,768 is 1.
Lets's calculate LCM of 402,912
2 | 402, 912 |
3 | 201, 456 |
67, 152 |
∴ So the LCM of the given numbers is 2 x 3 x 67 x 152 = 61104
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/61104
Therefore, the GCF of Fractions 269/402,768/912 is 1/61104
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 402,912 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(402,912) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(402,912) x common factors =6 x 1 = 6
LCM(402,912) = ( 402 × 912 ) / 6
LCM(402,912) = 366624 / 6
LCM(402,912) = 61104
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 269,768?
The HCF of 269,768 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 269/402, 768/912?
Answer: GCF of Numerators as per given numbers 269/402, 768/912 is
GCF of Numerators i.e. for 269,768 is 1
LCM of denominators i.e. for 402,912 is 61104.
Thus, GCF of Fractions is 1/61104.Finally, GCF of Fractions for 269/402, 768/912 is 1/61104.