Use our free GCF of Fractions Calculator tool to compute the GCF of 609/469, 680/756 i.e 1/50652 easily. The following is the detailed procedure to determine the greatest common factor of fractions 609/469, 680/756.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 609/469,680/756
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 609/469,680/756, numerators are 609,680
Denominators are 469,756
The GCF of 609,680 is 1 .
LCM of 469,756 is 50652.
The greatest common factor of 609/469,680/756 = [GCF of 609,680]/[LCM of 469,756]= 1/50652
Therefore, the GCF of 609/469,680/756 is 1/50652.
To find the highest common factor of 609,680, we have to find the factors of both numbers and list the highest common factor.
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The HCF of 609,680 is 1.
Lets's calculate GCF of 609,680
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Greatest Common Factor
We found the factors 609,680 . The biggest common factor number is the GCF number.
So the greatest common factor 609,680 is 1.
Lets's calculate LCM of 469,756
7 | 469, 756 |
67, 108 |
∴ So the LCM of the given numbers is 7 x 67 x 108 = 50652
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/50652
Therefore, the GCF of Fractions 609/469,680/756 is 1/50652
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 469,756 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(469,756) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(469,756) x common factors =7 x 1 = 7
LCM(469,756) = ( 469 × 756 ) / 7
LCM(469,756) = 354564 / 7
LCM(469,756) = 50652
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 609,680?
The HCF of 609,680 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 609/469, 680/756?
Answer: GCF of Numerators as per given numbers 609/469, 680/756 is
GCF of Numerators i.e. for 609,680 is 1
LCM of denominators i.e. for 469,756 is 50652.
Thus, GCF of Fractions is 1/50652.Finally, GCF of Fractions for 609/469, 680/756 is 1/50652.