Use our free GCF of Fractions Calculator tool to compute the GCF of 99/40, 749/98, 100/900 i.e 1/88200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 99/40, 749/98, 100/900.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 99/40,749/98,100/900
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 99/40,749/98,100/900, numerators are 99,749,100
Denominators are 40,98,900
The GCF of 99,749,100 is 1 .
LCM of 40,98,900 is 88200.
The greatest common factor of 99/40,749/98,100/900 = [GCF of 99,749,100]/[LCM of 40,98,900]= 1/88200
Therefore, the GCF of 99/40,749/98,100/900 is 1/88200.
To find the highest common factor of 99,749,100, we have to find the factors of both numbers and list the highest common factor.
The factors of 99 are 1, 3, 9, 11, 33, 99
The factors of 749 are 1, 7, 107, 749
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
The HCF of 99,749,100 is 1.
Lets's calculate GCF of 99,749,100
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 99
:1,3,9,11,33,99
Now, list down the factors of 749
:1,7,107,749
Now, list down the factors of 100
:1,2,4,5,10,20,25,50,100
Greatest Common Factor
We found the factors 99,749,100 . The biggest common factor number is the GCF number.
So the greatest common factor 99,749,100 is 1.
Lets's calculate LCM of 40,98,900
2 | 40, 98, 900 |
2 | 20, 49, 450 |
5 | 10, 49, 225 |
2, 49, 45 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 2 x 49 x 45 = 88200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/88200
Therefore, the GCF of Fractions 99/40,749/98,100/900 is 1/88200
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 40,98,900 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,98,900) = 2
common factors(in case of two or more numbers have common factors) = 20
GCF(40,98,900) x common factors =2 x 20 = 40
LCM(40,98,900) = ( 40 × 98 × 900 ) / 40
LCM(40,98,900) = 3528000 / 40
LCM(40,98,900) = 88200
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 99,749,100?
The HCF of 99,749,100 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 99/40, 749/98, 100/900?
Answer: GCF of Numerators as per given numbers 99/40, 749/98, 100/900 is
GCF of Numerators i.e. for 99,749,100 is 1
LCM of denominators i.e. for 40,98,900 is 88200.
Thus, GCF of Fractions is 1/88200.Finally, GCF of Fractions for 99/40, 749/98, 100/900 is 1/88200.