Use our free GCF of Fractions Calculator tool to compute the GCF of 766/618, 278/974 i.e 2/300966 easily. The following is the detailed procedure to determine the greatest common factor of fractions 766/618, 278/974.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 766/618,278/974
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 766/618,278/974, numerators are 766,278
Denominators are 618,974
The GCF of 766,278 is 2 .
LCM of 618,974 is 300966.
The greatest common factor of 766/618,278/974 = [GCF of 766,278]/[LCM of 618,974]= 2/300966
Therefore, the GCF of 766/618,278/974 is 2/300966.
To find the highest common factor of 766,278, we have to find the factors of both numbers and list the highest common factor.
The factors of 766 are 1, 2, 383, 766
The factors of 278 are 1, 2, 139, 278
The HCF of 766,278 is 2.
Lets's calculate GCF of 766,278
2 | 766, 278 |
383, 139 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 766
:1,2,383,766
Now, list down the factors of 278
:1,2,139,278
Greatest Common Factor
We found the factors 766,278 . The biggest common factor number is the GCF number.
So the greatest common factor 766,278 is 2.
Lets's calculate LCM of 618,974
2 | 618, 974 |
309, 487 |
∴ So the LCM of the given numbers is 2 x 309 x 487 = 300966
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/300966
Therefore, the GCF of Fractions 766/618,278/974 is 2/300966
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 618,974 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(618,974) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(618,974) x common factors =2 x 1 = 2
LCM(618,974) = ( 618 × 974 ) / 2
LCM(618,974) = 601932 / 2
LCM(618,974) = 300966
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 766,278?
The HCF of 766,278 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 766/618, 278/974?
Answer: GCF of Numerators as per given numbers 766/618, 278/974 is
GCF of Numerators i.e. for 766,278 is 2
LCM of denominators i.e. for 618,974 is 300966.
Thus, GCF of Fractions is 2/300966.Finally, GCF of Fractions for 766/618, 278/974 is 2/300966.