Use our free GCF of Fractions Calculator tool to compute the GCF of 15/54, 846/78, 219/676 i.e 3/18252 easily. The following is the detailed procedure to determine the greatest common factor of fractions 15/54, 846/78, 219/676.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 15/54,846/78,219/676
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 15/54,846/78,219/676, numerators are 15,846,219
Denominators are 54,78,676
The GCF of 15,846,219 is 3 .
LCM of 54,78,676 is 18252.
The greatest common factor of 15/54,846/78,219/676 = [GCF of 15,846,219]/[LCM of 54,78,676]= 3/18252
Therefore, the GCF of 15/54,846/78,219/676 is 3/18252.
To find the highest common factor of 15,846,219, 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 846 are 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846
The factors of 219 are 1, 3, 73, 219
The HCF of 15,846,219 is 3.
Lets's calculate GCF of 15,846,219
3 | 15, 846, 219 |
5, 282, 73 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 15
:1,3,5,15
Now, list down the factors of 846
:1,2,3,6,9,18,47,94,141,282,423,846
Now, list down the factors of 219
:1,3,73,219
Greatest Common Factor
We found the factors 15,846,219 . The biggest common factor number is the GCF number.
So the greatest common factor 15,846,219 is 3.
Lets's calculate LCM of 54,78,676
2 | 54, 78, 676 |
3 | 27, 39, 338 |
13 | 9, 13, 338 |
9, 1, 26 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 9 x 1 x 26 = 18252
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/18252
Therefore, the GCF of Fractions 15/54,846/78,219/676 is 3/18252
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 54,78,676 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,78,676) = 2
common factors(in case of two or more numbers have common factors) = 78
GCF(54,78,676) x common factors =2 x 78 = 156
LCM(54,78,676) = ( 54 × 78 × 676 ) / 156
LCM(54,78,676) = 2847312 / 156
LCM(54,78,676) = 18252
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 15,846,219?
The HCF of 15,846,219 is 3
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 15/54, 846/78, 219/676?
Answer: GCF of Numerators as per given numbers 15/54, 846/78, 219/676 is
GCF of Numerators i.e. for 15,846,219 is 3
LCM of denominators i.e. for 54,78,676 is 18252.
Thus, GCF of Fractions is 3/18252.Finally, GCF of Fractions for 15/54, 846/78, 219/676 is 3/18252.