Use our free GCF of Fractions Calculator tool to compute the GCF of 897/684, 123/774 i.e 3/29412 easily. The following is the detailed procedure to determine the greatest common factor of fractions 897/684, 123/774.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 897/684,123/774
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 897/684,123/774, numerators are 897,123
Denominators are 684,774
The GCF of 897,123 is 3 .
LCM of 684,774 is 29412.
The greatest common factor of 897/684,123/774 = [GCF of 897,123]/[LCM of 684,774]= 3/29412
Therefore, the GCF of 897/684,123/774 is 3/29412.
To find the highest common factor of 897,123, 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 123 are 1, 3, 41, 123
The HCF of 897,123 is 3.
Lets's calculate GCF of 897,123
3 | 897, 123 |
299, 41 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 897
:1,3,13,23,39,69,299,897
Now, list down the factors of 123
:1,3,41,123
Greatest Common Factor
We found the factors 897,123 . The biggest common factor number is the GCF number.
So the greatest common factor 897,123 is 3.
Lets's calculate LCM of 684,774
2 | 684, 774 |
3 | 342, 387 |
3 | 114, 129 |
38, 43 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 38 x 43 = 29412
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/29412
Therefore, the GCF of Fractions 897/684,123/774 is 3/29412
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 684,774 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(684,774) = 18
common factors(in case of two or more numbers have common factors) = 1
GCF(684,774) x common factors =18 x 1 = 18
LCM(684,774) = ( 684 × 774 ) / 18
LCM(684,774) = 529416 / 18
LCM(684,774) = 29412
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 897,123?
The HCF of 897,123 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 897/684, 123/774?
Answer: GCF of Numerators as per given numbers 897/684, 123/774 is
GCF of Numerators i.e. for 897,123 is 3
LCM of denominators i.e. for 684,774 is 29412.
Thus, GCF of Fractions is 3/29412.Finally, GCF of Fractions for 897/684, 123/774 is 3/29412.