Use our free GCF of Fractions Calculator tool to compute the GCF of 5/40, 9/50, 5/32, 64/410 i.e 1/32800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5/40, 9/50, 5/32, 64/410.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 5/40,9/50,5/32,64/410
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 5/40,9/50,5/32,64/410, numerators are 5,9,5,64
Denominators are 40,50,32,410
The GCF of 5,9,5,64 is 1 .
LCM of 40,50,32,410 is 32800.
The greatest common factor of 5/40,9/50,5/32,64/410 = [GCF of 5,9,5,64]/[LCM of 40,50,32,410]= 1/32800
Therefore, the GCF of 5/40,9/50,5/32,64/410 is 1/32800.
To find the highest common factor of 5,9,5,64, we have to find the factors of both numbers and list the highest common factor.
The factors of 5 are 1, 5
The factors of 9 are 1, 3, 9
The factors of 5 are 1, 5
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The HCF of 5,9,5,64 is 1.
Lets's calculate GCF of 5,9,5,64
∴ So GCF of numbers is 1 because of no common factors present between them.
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 5
:1,5
Now, list down the factors of 64
:1,2,4,8,16,32,64
Greatest Common Factor
We found the factors 5,9,5,64 . The biggest common factor number is the GCF number.
So the greatest common factor 5,9,5,64 is 1.
Lets's calculate LCM of 40,50,32,410
2 | 40, 50, 32, 410 |
2 | 20, 25, 16, 205 |
2 | 10, 25, 8, 205 |
5 | 5, 25, 4, 205 |
1, 5, 4, 41 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 1 x 5 x 4 x 41 = 32800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/32800
Therefore, the GCF of Fractions 5/40,9/50,5/32,64/410 is 1/32800
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 40,50,32,410 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,50,32,410) = 2
common factors(in case of two or more numbers have common factors) = 400
GCF(40,50,32,410) x common factors =2 x 400 = 800
LCM(40,50,32,410) = ( 40 × 50 × 32 × 410 ) / 800
LCM(40,50,32,410) = 26240000 / 800
LCM(40,50,32,410) = 32800
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 5,9,5,64?
The HCF of 5,9,5,64 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 5/40, 9/50, 5/32, 64/410?
Answer: GCF of Numerators as per given numbers 5/40, 9/50, 5/32, 64/410 is
GCF of Numerators i.e. for 5,9,5,64 is 1
LCM of denominators i.e. for 40,50,32,410 is 32800.
Thus, GCF of Fractions is 1/32800.Finally, GCF of Fractions for 5/40, 9/50, 5/32, 64/410 is 1/32800.