Use our free GCF of Fractions Calculator tool to compute the GCF of 106/564, 697/296 i.e 1/41736 easily. The following is the detailed procedure to determine the greatest common factor of fractions 106/564, 697/296.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 106/564,697/296
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 106/564,697/296, numerators are 106,697
Denominators are 564,296
The GCF of 106,697 is 1 .
LCM of 564,296 is 41736.
The greatest common factor of 106/564,697/296 = [GCF of 106,697]/[LCM of 564,296]= 1/41736
Therefore, the GCF of 106/564,697/296 is 1/41736.
To find the highest common factor of 106,697, we have to find the factors of both numbers and list the highest common factor.
The factors of 106 are 1, 2, 53, 106
The factors of 697 are 1, 17, 41, 697
The HCF of 106,697 is 1.
Lets's calculate GCF of 106,697
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 106
:1,2,53,106
Now, list down the factors of 697
:1,17,41,697
Greatest Common Factor
We found the factors 106,697 . The biggest common factor number is the GCF number.
So the greatest common factor 106,697 is 1.
Lets's calculate LCM of 564,296
2 | 564, 296 |
2 | 282, 148 |
141, 74 |
∴ So the LCM of the given numbers is 2 x 2 x 141 x 74 = 41736
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/41736
Therefore, the GCF of Fractions 106/564,697/296 is 1/41736
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 564,296 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,296) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(564,296) x common factors =4 x 1 = 4
LCM(564,296) = ( 564 × 296 ) / 4
LCM(564,296) = 166944 / 4
LCM(564,296) = 41736
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 106,697?
The HCF of 106,697 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 106/564, 697/296?
Answer: GCF of Numerators as per given numbers 106/564, 697/296 is
GCF of Numerators i.e. for 106,697 is 1
LCM of denominators i.e. for 564,296 is 41736.
Thus, GCF of Fractions is 1/41736.Finally, GCF of Fractions for 106/564, 697/296 is 1/41736.