Use our free GCF of Fractions Calculator tool to compute the GCF of 308/678, 2778/2068 i.e 2/701052 easily. The following is the detailed procedure to determine the greatest common factor of fractions 308/678, 2778/2068.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 308/678,2778/2068
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 308/678,2778/2068, numerators are 308,2778
Denominators are 678,2068
The GCF of 308,2778 is 2 .
LCM of 678,2068 is 701052.
The greatest common factor of 308/678,2778/2068 = [GCF of 308,2778]/[LCM of 678,2068]= 2/701052
Therefore, the GCF of 308/678,2778/2068 is 2/701052.
To find the highest common factor of 308,2778, we have to find the factors of both numbers and list the highest common factor.
The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
The factors of 2778 are 1, 2, 3, 6, 463, 926, 1389, 2778
The HCF of 308,2778 is 2.
Lets's calculate GCF of 308,2778
2 | 308, 2778 |
154, 1389 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 308
:1,2,4,7,11,14,22,28,44,77,154,308
Now, list down the factors of 2778
:1,2,3,6,463,926,1389,2778
Greatest Common Factor
We found the factors 308,2778 . The biggest common factor number is the GCF number.
So the greatest common factor 308,2778 is 2.
Lets's calculate LCM of 678,2068
2 | 678, 2068 |
339, 1034 |
∴ So the LCM of the given numbers is 2 x 339 x 1034 = 701052
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/701052
Therefore, the GCF of Fractions 308/678,2778/2068 is 2/701052
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 678,2068 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,2068) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(678,2068) x common factors =2 x 1 = 2
LCM(678,2068) = ( 678 × 2068 ) / 2
LCM(678,2068) = 1402104 / 2
LCM(678,2068) = 701052
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 308,2778?
The HCF of 308,2778 is 2
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 308/678, 2778/2068?
Answer: GCF of Numerators as per given numbers 308/678, 2778/2068 is
GCF of Numerators i.e. for 308,2778 is 2
LCM of denominators i.e. for 678,2068 is 701052.
Thus, GCF of Fractions is 2/701052.Finally, GCF of Fractions for 308/678, 2778/2068 is 2/701052.