Use our free GCF of Fractions Calculator tool to compute the GCF of 900/785, 132/406 i.e 12/318710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 900/785, 132/406.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 900/785,132/406
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 900/785,132/406, numerators are 900,132
Denominators are 785,406
The GCF of 900,132 is 12 .
LCM of 785,406 is 318710.
The greatest common factor of 900/785,132/406 = [GCF of 900,132]/[LCM of 785,406]= 12/318710
Therefore, the GCF of 900/785,132/406 is 12/318710.
To find the highest common factor of 900,132, we have to find the factors of both numbers and list the highest common factor.
The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The HCF of 900,132 is 12.
Lets's calculate GCF of 900,132
2 | 900, 132 |
2 | 450, 66 |
3 | 225, 33 |
75, 11 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 900
:1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900
Now, list down the factors of 132
:1,2,3,4,6,11,12,22,33,44,66,132
Greatest Common Factor
We found the factors 900,132 . The biggest common factor number is the GCF number.
So the greatest common factor 900,132 is 12.
Lets's calculate LCM of 785,406
Given numbers has no common factors except 1. So, there LCM is their product i.e 318710
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/318710
Therefore, the GCF of Fractions 900/785,132/406 is 12/318710
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 785,406 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(785,406) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(785,406) x common factors =1 x 1 = 1
LCM(785,406) = ( 785 × 406 ) / 1
LCM(785,406) = 318710 / 1
LCM(785,406) = 318710
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 900,132?
The HCF of 900,132 is 12
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 900/785, 132/406?
Answer: GCF of Numerators as per given numbers 900/785, 132/406 is
GCF of Numerators i.e. for 900,132 is 12
LCM of denominators i.e. for 785,406 is 318710.
Thus, GCF of Fractions is 12/318710.Finally, GCF of Fractions for 900/785, 132/406 is 12/318710.