Use our free GCF of Fractions Calculator tool to compute the GCF of 72/864, 609/298, 774/756 i.e 3/901152 easily. The following is the detailed procedure to determine the greatest common factor of fractions 72/864, 609/298, 774/756.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 72/864,609/298,774/756
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 72/864,609/298,774/756, numerators are 72,609,774
Denominators are 864,298,756
The GCF of 72,609,774 is 3 .
LCM of 864,298,756 is 901152.
The greatest common factor of 72/864,609/298,774/756 = [GCF of 72,609,774]/[LCM of 864,298,756]= 3/901152
Therefore, the GCF of 72/864,609/298,774/756 is 3/901152.
To find the highest common factor of 72,609,774, we have to find the factors of both numbers and list the highest common factor.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The HCF of 72,609,774 is 3.
Lets's calculate GCF of 72,609,774
3 | 72, 609, 774 |
24, 203, 258 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Greatest Common Factor
We found the factors 72,609,774 . The biggest common factor number is the GCF number.
So the greatest common factor 72,609,774 is 3.
Lets's calculate LCM of 864,298,756
2 | 864, 298, 756 |
2 | 432, 149, 378 |
3 | 216, 149, 189 |
3 | 72, 149, 63 |
3 | 24, 149, 21 |
8, 149, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 3 x 8 x 149 x 7 = 901152
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/901152
Therefore, the GCF of Fractions 72/864,609/298,774/756 is 3/901152
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 864,298,756 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(864,298,756) = 2
common factors(in case of two or more numbers have common factors) = 108
GCF(864,298,756) x common factors =2 x 108 = 216
LCM(864,298,756) = ( 864 × 298 × 756 ) / 216
LCM(864,298,756) = 194648832 / 216
LCM(864,298,756) = 901152
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 72,609,774?
The HCF of 72,609,774 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 72/864, 609/298, 774/756?
Answer: GCF of Numerators as per given numbers 72/864, 609/298, 774/756 is
GCF of Numerators i.e. for 72,609,774 is 3
LCM of denominators i.e. for 864,298,756 is 901152.
Thus, GCF of Fractions is 3/901152.Finally, GCF of Fractions for 72/864, 609/298, 774/756 is 3/901152.