Use our free GCF of Fractions Calculator tool to compute the GCF of 8/28, 5/10, 9/32, 75/782 i.e 1/437920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/28, 5/10, 9/32, 75/782.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 8/28,5/10,9/32,75/782
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 8/28,5/10,9/32,75/782, numerators are 8,5,9,75
Denominators are 28,10,32,782
The GCF of 8,5,9,75 is 1 .
LCM of 28,10,32,782 is 437920.
The greatest common factor of 8/28,5/10,9/32,75/782 = [GCF of 8,5,9,75]/[LCM of 28,10,32,782]= 1/437920
Therefore, the GCF of 8/28,5/10,9/32,75/782 is 1/437920.
To find the highest common factor of 8,5,9,75, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 5 are 1, 5
The factors of 9 are 1, 3, 9
The factors of 75 are 1, 3, 5, 15, 25, 75
The HCF of 8,5,9,75 is 1.
Lets's calculate GCF of 8,5,9,75
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 5
:1,5
Now, list down the factors of 9
:1,3,9
Now, list down the factors of 75
:1,3,5,15,25,75
Greatest Common Factor
We found the factors 8,5,9,75 . The biggest common factor number is the GCF number.
So the greatest common factor 8,5,9,75 is 1.
Lets's calculate LCM of 28,10,32,782
2 | 28, 10, 32, 782 |
2 | 14, 5, 16, 391 |
7, 5, 8, 391 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 5 x 8 x 391 = 437920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/437920
Therefore, the GCF of Fractions 8/28,5/10,9/32,75/782 is 1/437920
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 28,10,32,782 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,10,32,782) = 2
common factors(in case of two or more numbers have common factors) = 8
GCF(28,10,32,782) x common factors =2 x 8 = 16
LCM(28,10,32,782) = ( 28 × 10 × 32 × 782 ) / 16
LCM(28,10,32,782) = 7006720 / 16
LCM(28,10,32,782) = 437920
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 8,5,9,75?
The HCF of 8,5,9,75 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 8/28, 5/10, 9/32, 75/782?
Answer: GCF of Numerators as per given numbers 8/28, 5/10, 9/32, 75/782 is
GCF of Numerators i.e. for 8,5,9,75 is 1
LCM of denominators i.e. for 28,10,32,782 is 437920.
Thus, GCF of Fractions is 1/437920.Finally, GCF of Fractions for 8/28, 5/10, 9/32, 75/782 is 1/437920.