Use our free GCF of Fractions Calculator tool to compute the GCF of 896/819, 256/633 i.e 128/172809 easily. The following is the detailed procedure to determine the greatest common factor of fractions 896/819, 256/633.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 896/819,256/633
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 896/819,256/633, numerators are 896,256
Denominators are 819,633
The GCF of 896,256 is 128 .
LCM of 819,633 is 172809.
The greatest common factor of 896/819,256/633 = [GCF of 896,256]/[LCM of 819,633]= 128/172809
Therefore, the GCF of 896/819,256/633 is 128/172809.
To find the highest common factor of 896,256, we have to find the factors of both numbers and list the highest common factor.
The factors of 896 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896
The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256
The HCF of 896,256 is 128.
Lets's calculate GCF of 896,256
2 | 896, 256 |
2 | 448, 128 |
2 | 224, 64 |
2 | 112, 32 |
2 | 56, 16 |
2 | 28, 8 |
2 | 14, 4 |
7, 2 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128
Now, list down the factors of 896
:1,2,4,7,8,14,16,28,32,56,64,112,128,224,448,896
Now, list down the factors of 256
:1,2,4,8,16,32,64,128,256
Greatest Common Factor
We found the factors 896,256 . The biggest common factor number is the GCF number.
So the greatest common factor 896,256 is 128.
Lets's calculate LCM of 819,633
3 | 819, 633 |
273, 211 |
∴ So the LCM of the given numbers is 3 x 273 x 211 = 172809
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 128/172809
Therefore, the GCF of Fractions 896/819,256/633 is 128/172809
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 819,633 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(819,633) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(819,633) x common factors =3 x 1 = 3
LCM(819,633) = ( 819 × 633 ) / 3
LCM(819,633) = 518427 / 3
LCM(819,633) = 172809
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 896,256?
The HCF of 896,256 is 128
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 896/819, 256/633?
Answer: GCF of Numerators as per given numbers 896/819, 256/633 is
GCF of Numerators i.e. for 896,256 is 128
LCM of denominators i.e. for 819,633 is 172809.
Thus, GCF of Fractions is 128/172809.Finally, GCF of Fractions for 896/819, 256/633 is 128/172809.