Use our free GCF of Fractions Calculator tool to compute the GCF of 15/71, 678/66, 686/144 i.e 1/112464 easily. The following is the detailed procedure to determine the greatest common factor of fractions 15/71, 678/66, 686/144.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 15/71,678/66,686/144
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 15/71,678/66,686/144, numerators are 15,678,686
Denominators are 71,66,144
The GCF of 15,678,686 is 1 .
LCM of 71,66,144 is 112464.
The greatest common factor of 15/71,678/66,686/144 = [GCF of 15,678,686]/[LCM of 71,66,144]= 1/112464
Therefore, the GCF of 15/71,678/66,686/144 is 1/112464.
To find the highest common factor of 15,678,686, we have to find the factors of both numbers and list the highest common factor.
The factors of 15 are 1, 3, 5, 15
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686
The HCF of 15,678,686 is 1.
Lets's calculate GCF of 15,678,686
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 15
:1,3,5,15
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Now, list down the factors of 686
:1,2,7,14,49,98,343,686
Greatest Common Factor
We found the factors 15,678,686 . The biggest common factor number is the GCF number.
So the greatest common factor 15,678,686 is 1.
Lets's calculate LCM of 71,66,144
2 | 71, 66, 144 |
3 | 71, 33, 72 |
71, 11, 24 |
∴ So the LCM of the given numbers is 2 x 3 x 71 x 11 x 24 = 112464
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/112464
Therefore, the GCF of Fractions 15/71,678/66,686/144 is 1/112464
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 71,66,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,66,144) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(71,66,144) x common factors =1 x 6 = 6
LCM(71,66,144) = ( 71 × 66 × 144 ) / 6
LCM(71,66,144) = 674784 / 6
LCM(71,66,144) = 112464
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 15,678,686?
The HCF of 15,678,686 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 15/71, 678/66, 686/144?
Answer: GCF of Numerators as per given numbers 15/71, 678/66, 686/144 is
GCF of Numerators i.e. for 15,678,686 is 1
LCM of denominators i.e. for 71,66,144 is 112464.
Thus, GCF of Fractions is 1/112464.Finally, GCF of Fractions for 15/71, 678/66, 686/144 is 1/112464.