Use our free GCF of Fractions Calculator tool to compute the GCF of 564/854, 896/816 i.e 4/348432 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/854, 896/816.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 564/854,896/816
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 564/854,896/816, numerators are 564,896
Denominators are 854,816
The GCF of 564,896 is 4 .
LCM of 854,816 is 348432.
The greatest common factor of 564/854,896/816 = [GCF of 564,896]/[LCM of 854,816]= 4/348432
Therefore, the GCF of 564/854,896/816 is 4/348432.
To find the highest common factor of 564,896, we have to find the factors of both numbers and list the highest common factor.
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The factors of 896 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896
The HCF of 564,896 is 4.
Lets's calculate GCF of 564,896
2 | 564, 896 |
2 | 282, 448 |
141, 224 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Now, list down the factors of 896
:1,2,4,7,8,14,16,28,32,56,64,112,128,224,448,896
Greatest Common Factor
We found the factors 564,896 . The biggest common factor number is the GCF number.
So the greatest common factor 564,896 is 4.
Lets's calculate LCM of 854,816
2 | 854, 816 |
427, 408 |
∴ So the LCM of the given numbers is 2 x 427 x 408 = 348432
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/348432
Therefore, the GCF of Fractions 564/854,896/816 is 4/348432
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 854,816 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(854,816) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(854,816) x common factors =2 x 1 = 2
LCM(854,816) = ( 854 × 816 ) / 2
LCM(854,816) = 696864 / 2
LCM(854,816) = 348432
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 564,896?
The HCF of 564,896 is 4
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 564/854, 896/816?
Answer: GCF of Numerators as per given numbers 564/854, 896/816 is
GCF of Numerators i.e. for 564,896 is 4
LCM of denominators i.e. for 854,816 is 348432.
Thus, GCF of Fractions is 4/348432.Finally, GCF of Fractions for 564/854, 896/816 is 4/348432.