Use our free GCF of Fractions Calculator tool to compute the GCF of 787/32, 296/24, 612/34 i.e 1/1632 easily. The following is the detailed procedure to determine the greatest common factor of fractions 787/32, 296/24, 612/34.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 787/32,296/24,612/34
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 787/32,296/24,612/34, numerators are 787,296,612
Denominators are 32,24,34
The GCF of 787,296,612 is 1 .
LCM of 32,24,34 is 1632.
The greatest common factor of 787/32,296/24,612/34 = [GCF of 787,296,612]/[LCM of 32,24,34]= 1/1632
Therefore, the GCF of 787/32,296/24,612/34 is 1/1632.
To find the highest common factor of 787,296,612, we have to find the factors of both numbers and list the highest common factor.
The factors of 787 are 1, 787
The factors of 296 are 1, 2, 4, 8, 37, 74, 148, 296
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The HCF of 787,296,612 is 1.
Lets's calculate GCF of 787,296,612
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 787
:1,787
Now, list down the factors of 296
:1,2,4,8,37,74,148,296
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Greatest Common Factor
We found the factors 787,296,612 . The biggest common factor number is the GCF number.
So the greatest common factor 787,296,612 is 1.
Lets's calculate LCM of 32,24,34
2 | 32, 24, 34 |
2 | 16, 12, 17 |
2 | 8, 6, 17 |
4, 3, 17 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 4 x 3 x 17 = 1632
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1632
Therefore, the GCF of Fractions 787/32,296/24,612/34 is 1/1632
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 32,24,34 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,24,34) = 2
common factors(in case of two or more numbers have common factors) = 8
GCF(32,24,34) x common factors =2 x 8 = 16
LCM(32,24,34) = ( 32 × 24 × 34 ) / 16
LCM(32,24,34) = 26112 / 16
LCM(32,24,34) = 1632
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 787,296,612?
The HCF of 787,296,612 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 787/32, 296/24, 612/34?
Answer: GCF of Numerators as per given numbers 787/32, 296/24, 612/34 is
GCF of Numerators i.e. for 787,296,612 is 1
LCM of denominators i.e. for 32,24,34 is 1632.
Thus, GCF of Fractions is 1/1632.Finally, GCF of Fractions for 787/32, 296/24, 612/34 is 1/1632.