Use our free GCF of Fractions Calculator tool to compute the GCF of 909/689, 165/912 i.e 3/628368 easily. The following is the detailed procedure to determine the greatest common factor of fractions 909/689, 165/912.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 909/689,165/912
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 909/689,165/912, numerators are 909,165
Denominators are 689,912
The GCF of 909,165 is 3 .
LCM of 689,912 is 628368.
The greatest common factor of 909/689,165/912 = [GCF of 909,165]/[LCM of 689,912]= 3/628368
Therefore, the GCF of 909/689,165/912 is 3/628368.
To find the highest common factor of 909,165, we have to find the factors of both numbers and list the highest common factor.
The factors of 909 are 1, 3, 9, 101, 303, 909
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165
The HCF of 909,165 is 3.
Lets's calculate GCF of 909,165
3 | 909, 165 |
303, 55 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 909
:1,3,9,101,303,909
Now, list down the factors of 165
:1,3,5,11,15,33,55,165
Greatest Common Factor
We found the factors 909,165 . The biggest common factor number is the GCF number.
So the greatest common factor 909,165 is 3.
Lets's calculate LCM of 689,912
Given numbers has no common factors except 1. So, there LCM is their product i.e 628368
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/628368
Therefore, the GCF of Fractions 909/689,165/912 is 3/628368
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 689,912 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(689,912) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(689,912) x common factors =1 x 1 = 1
LCM(689,912) = ( 689 × 912 ) / 1
LCM(689,912) = 628368 / 1
LCM(689,912) = 628368
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 909,165?
The HCF of 909,165 is 3
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 909/689, 165/912?
Answer: GCF of Numerators as per given numbers 909/689, 165/912 is
GCF of Numerators i.e. for 909,165 is 3
LCM of denominators i.e. for 689,912 is 628368.
Thus, GCF of Fractions is 3/628368.Finally, GCF of Fractions for 909/689, 165/912 is 3/628368.