Use our free GCF of Fractions Calculator tool to compute the GCF of 69/31, 21/397, 806/754 i.e 1/9279478 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/31, 21/397, 806/754.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 69/31,21/397,806/754
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 69/31,21/397,806/754, numerators are 69,21,806
Denominators are 31,397,754
The GCF of 69,21,806 is 1 .
LCM of 31,397,754 is 9279478.
The greatest common factor of 69/31,21/397,806/754 = [GCF of 69,21,806]/[LCM of 31,397,754]= 1/9279478
Therefore, the GCF of 69/31,21/397,806/754 is 1/9279478.
To find the highest common factor of 69,21,806, we have to find the factors of both numbers and list the highest common factor.
The factors of 69 are 1, 3, 23, 69
The factors of 21 are 1, 3, 7, 21
The factors of 806 are 1, 2, 13, 26, 31, 62, 403, 806
The HCF of 69,21,806 is 1.
Lets's calculate GCF of 69,21,806
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 806
:1,2,13,26,31,62,403,806
Greatest Common Factor
We found the factors 69,21,806 . The biggest common factor number is the GCF number.
So the greatest common factor 69,21,806 is 1.
Lets's calculate LCM of 31,397,754
Given numbers has no common factors except 1. So, there LCM is their product i.e 9279478
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9279478
Therefore, the GCF of Fractions 69/31,21/397,806/754 is 1/9279478
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 31,397,754 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,397,754) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,397,754) x common factors =1 x 1 = 1
LCM(31,397,754) = ( 31 × 397 × 754 ) / 1
LCM(31,397,754) = 9279478 / 1
LCM(31,397,754) = 9279478
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 69,21,806?
The HCF of 69,21,806 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 69/31, 21/397, 806/754?
Answer: GCF of Numerators as per given numbers 69/31, 21/397, 806/754 is
GCF of Numerators i.e. for 69,21,806 is 1
LCM of denominators i.e. for 31,397,754 is 9279478.
Thus, GCF of Fractions is 1/9279478.Finally, GCF of Fractions for 69/31, 21/397, 806/754 is 1/9279478.