Use our free GCF of Fractions Calculator tool to compute the GCF of 109/982, 165/140 i.e 1/68740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 109/982, 165/140.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 109/982,165/140
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 109/982,165/140, numerators are 109,165
Denominators are 982,140
The GCF of 109,165 is 1 .
LCM of 982,140 is 68740.
The greatest common factor of 109/982,165/140 = [GCF of 109,165]/[LCM of 982,140]= 1/68740
Therefore, the GCF of 109/982,165/140 is 1/68740.
To find the highest common factor of 109,165, we have to find the factors of both numbers and list the highest common factor.
The factors of 109 are 1, 109
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165
The HCF of 109,165 is 1.
Lets's calculate GCF of 109,165
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 109
:1,109
Now, list down the factors of 165
:1,3,5,11,15,33,55,165
Greatest Common Factor
We found the factors 109,165 . The biggest common factor number is the GCF number.
So the greatest common factor 109,165 is 1.
Lets's calculate LCM of 982,140
2 | 982, 140 |
491, 70 |
∴ So the LCM of the given numbers is 2 x 491 x 70 = 68740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/68740
Therefore, the GCF of Fractions 109/982,165/140 is 1/68740
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 982,140 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(982,140) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(982,140) x common factors =2 x 1 = 2
LCM(982,140) = ( 982 × 140 ) / 2
LCM(982,140) = 137480 / 2
LCM(982,140) = 68740
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 109,165?
The HCF of 109,165 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 109/982, 165/140?
Answer: GCF of Numerators as per given numbers 109/982, 165/140 is
GCF of Numerators i.e. for 109,165 is 1
LCM of denominators i.e. for 982,140 is 68740.
Thus, GCF of Fractions is 1/68740.Finally, GCF of Fractions for 109/982, 165/140 is 1/68740.