Use our free GCF of Fractions Calculator tool to compute the GCF of 78/54, 667/61, 261/459 i.e 1/55998 easily. The following is the detailed procedure to determine the greatest common factor of fractions 78/54, 667/61, 261/459.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 78/54,667/61,261/459
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 78/54,667/61,261/459, numerators are 78,667,261
Denominators are 54,61,459
The GCF of 78,667,261 is 1 .
LCM of 54,61,459 is 55998.
The greatest common factor of 78/54,667/61,261/459 = [GCF of 78,667,261]/[LCM of 54,61,459]= 1/55998
Therefore, the GCF of 78/54,667/61,261/459 is 1/55998.
To find the highest common factor of 78,667,261, we have to find the factors of both numbers and list the highest common factor.
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The factors of 667 are 1, 23, 29, 667
The factors of 261 are 1, 3, 9, 29, 87, 261
The HCF of 78,667,261 is 1.
Lets's calculate GCF of 78,667,261
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Now, list down the factors of 667
:1,23,29,667
Now, list down the factors of 261
:1,3,9,29,87,261
Greatest Common Factor
We found the factors 78,667,261 . The biggest common factor number is the GCF number.
So the greatest common factor 78,667,261 is 1.
Lets's calculate LCM of 54,61,459
3 | 54, 61, 459 |
3 | 18, 61, 153 |
3 | 6, 61, 51 |
2, 61, 17 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 2 x 61 x 17 = 55998
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/55998
Therefore, the GCF of Fractions 78/54,667/61,261/459 is 1/55998
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 54,61,459 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,61,459) = 1
common factors(in case of two or more numbers have common factors) = 27
GCF(54,61,459) x common factors =1 x 27 = 27
LCM(54,61,459) = ( 54 × 61 × 459 ) / 27
LCM(54,61,459) = 1511946 / 27
LCM(54,61,459) = 55998
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 78,667,261?
The HCF of 78,667,261 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 78/54, 667/61, 261/459?
Answer: GCF of Numerators as per given numbers 78/54, 667/61, 261/459 is
GCF of Numerators i.e. for 78,667,261 is 1
LCM of denominators i.e. for 54,61,459 is 55998.
Thus, GCF of Fractions is 1/55998.Finally, GCF of Fractions for 78/54, 667/61, 261/459 is 1/55998.