Use our free GCF of Fractions Calculator tool to compute the GCF of 66/823, 78/319 i.e 6/262537 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/823, 78/319.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 66/823,78/319
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 66/823,78/319, numerators are 66,78
Denominators are 823,319
The GCF of 66,78 is 6 .
LCM of 823,319 is 262537.
The greatest common factor of 66/823,78/319 = [GCF of 66,78]/[LCM of 823,319]= 6/262537
Therefore, the GCF of 66/823,78/319 is 6/262537.
To find the highest common factor of 66,78, we have to find the factors of both numbers and list the highest common factor.
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The HCF of 66,78 is 6.
Lets's calculate GCF of 66,78
2 | 66, 78 |
3 | 33, 39 |
11, 13 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Greatest Common Factor
We found the factors 66,78 . The biggest common factor number is the GCF number.
So the greatest common factor 66,78 is 6.
Lets's calculate LCM of 823,319
Given numbers has no common factors except 1. So, there LCM is their product i.e 262537
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/262537
Therefore, the GCF of Fractions 66/823,78/319 is 6/262537
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 823,319 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(823,319) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(823,319) x common factors =1 x 1 = 1
LCM(823,319) = ( 823 × 319 ) / 1
LCM(823,319) = 262537 / 1
LCM(823,319) = 262537
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 66,78?
The HCF of 66,78 is 6
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 66/823, 78/319?
Answer: GCF of Numerators as per given numbers 66/823, 78/319 is
GCF of Numerators i.e. for 66,78 is 6
LCM of denominators i.e. for 823,319 is 262537.
Thus, GCF of Fractions is 6/262537.Finally, GCF of Fractions for 66/823, 78/319 is 6/262537.