Use our free GCF of Fractions Calculator tool to compute the GCF of 14/72, 609/78, 913/178 i.e 1/83304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/72, 609/78, 913/178.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/72,609/78,913/178
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 14/72,609/78,913/178, numerators are 14,609,913
Denominators are 72,78,178
The GCF of 14,609,913 is 1 .
LCM of 72,78,178 is 83304.
The greatest common factor of 14/72,609/78,913/178 = [GCF of 14,609,913]/[LCM of 72,78,178]= 1/83304
Therefore, the GCF of 14/72,609/78,913/178 is 1/83304.
To find the highest common factor of 14,609,913, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
The factors of 913 are 1, 11, 83, 913
The HCF of 14,609,913 is 1.
Lets's calculate GCF of 14,609,913
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
Now, list down the factors of 913
:1,11,83,913
Greatest Common Factor
We found the factors 14,609,913 . The biggest common factor number is the GCF number.
So the greatest common factor 14,609,913 is 1.
Lets's calculate LCM of 72,78,178
2 | 72, 78, 178 |
3 | 36, 39, 89 |
12, 13, 89 |
∴ So the LCM of the given numbers is 2 x 3 x 12 x 13 x 89 = 83304
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/83304
Therefore, the GCF of Fractions 14/72,609/78,913/178 is 1/83304
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 72,78,178 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(72,78,178) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(72,78,178) x common factors =2 x 6 = 12
LCM(72,78,178) = ( 72 × 78 × 178 ) / 12
LCM(72,78,178) = 999648 / 12
LCM(72,78,178) = 83304
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 14,609,913?
The HCF of 14,609,913 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 14/72, 609/78, 913/178?
Answer: GCF of Numerators as per given numbers 14/72, 609/78, 913/178 is
GCF of Numerators i.e. for 14,609,913 is 1
LCM of denominators i.e. for 72,78,178 is 83304.
Thus, GCF of Fractions is 1/83304.Finally, GCF of Fractions for 14/72, 609/78, 913/178 is 1/83304.