Use our free GCF of Fractions Calculator tool to compute the GCF of 897/168, 858/735 i.e 39/5880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 897/168, 858/735.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 897/168,858/735
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 897/168,858/735, numerators are 897,858
Denominators are 168,735
The GCF of 897,858 is 39 .
LCM of 168,735 is 5880.
The greatest common factor of 897/168,858/735 = [GCF of 897,858]/[LCM of 168,735]= 39/5880
Therefore, the GCF of 897/168,858/735 is 39/5880.
To find the highest common factor of 897,858, we have to find the factors of both numbers and list the highest common factor.
The factors of 897 are 1, 3, 13, 23, 39, 69, 299, 897
The factors of 858 are 1, 2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858
The HCF of 897,858 is 39.
Lets's calculate GCF of 897,858
3 | 897, 858 |
13 | 299, 286 |
23, 22 |
∴ So the GCF of the given numbers is 3 x 13 = 39
Now, list down the factors of 897
:1,3,13,23,39,69,299,897
Now, list down the factors of 858
:1,2,3,6,11,13,22,26,33,39,66,78,143,286,429,858
Greatest Common Factor
We found the factors 897,858 . The biggest common factor number is the GCF number.
So the greatest common factor 897,858 is 39.
Lets's calculate LCM of 168,735
3 | 168, 735 |
7 | 56, 245 |
8, 35 |
∴ So the LCM of the given numbers is 3 x 7 x 8 x 35 = 5880
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 39/5880
Therefore, the GCF of Fractions 897/168,858/735 is 39/5880
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 168,735 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(168,735) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(168,735) x common factors =21 x 1 = 21
LCM(168,735) = ( 168 × 735 ) / 21
LCM(168,735) = 123480 / 21
LCM(168,735) = 5880
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 897,858?
The HCF of 897,858 is 39
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 897/168, 858/735?
Answer: GCF of Numerators as per given numbers 897/168, 858/735 is
GCF of Numerators i.e. for 897,858 is 39
LCM of denominators i.e. for 168,735 is 5880.
Thus, GCF of Fractions is 39/5880.Finally, GCF of Fractions for 897/168, 858/735 is 39/5880.