Use our free GCF of Fractions Calculator tool to compute the GCF of 65/100, 33/342, 812/420 i.e 1/119700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 65/100, 33/342, 812/420.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 65/100,33/342,812/420
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 65/100,33/342,812/420, numerators are 65,33,812
Denominators are 100,342,420
The GCF of 65,33,812 is 1 .
LCM of 100,342,420 is 119700.
The greatest common factor of 65/100,33/342,812/420 = [GCF of 65,33,812]/[LCM of 100,342,420]= 1/119700
Therefore, the GCF of 65/100,33/342,812/420 is 1/119700.
To find the highest common factor of 65,33,812, we have to find the factors of both numbers and list the highest common factor.
The factors of 65 are 1, 5, 13, 65
The factors of 33 are 1, 3, 11, 33
The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
The HCF of 65,33,812 is 1.
Lets's calculate GCF of 65,33,812
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 65
:1,5,13,65
Now, list down the factors of 33
:1,3,11,33
Now, list down the factors of 812
:1,2,4,7,14,28,29,58,116,203,406,812
Greatest Common Factor
We found the factors 65,33,812 . The biggest common factor number is the GCF number.
So the greatest common factor 65,33,812 is 1.
Lets's calculate LCM of 100,342,420
2 | 100, 342, 420 |
2 | 50, 171, 210 |
3 | 25, 171, 105 |
5 | 25, 57, 35 |
5, 57, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 5 x 57 x 7 = 119700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/119700
Therefore, the GCF of Fractions 65/100,33/342,812/420 is 1/119700
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 100,342,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(100,342,420) = 2
common factors(in case of two or more numbers have common factors) = 60
GCF(100,342,420) x common factors =2 x 60 = 120
LCM(100,342,420) = ( 100 × 342 × 420 ) / 120
LCM(100,342,420) = 14364000 / 120
LCM(100,342,420) = 119700
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 65,33,812?
The HCF of 65,33,812 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 65/100, 33/342, 812/420?
Answer: GCF of Numerators as per given numbers 65/100, 33/342, 812/420 is
GCF of Numerators i.e. for 65,33,812 is 1
LCM of denominators i.e. for 100,342,420 is 119700.
Thus, GCF of Fractions is 1/119700.Finally, GCF of Fractions for 65/100, 33/342, 812/420 is 1/119700.