GCF of 109/65, 105/2112
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 109/65, 105/2112 i.e 1/137280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 109/65, 105/2112.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 109/65,105/2112?
Given fractions are 109/65,105/2112
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 109/65,105/2112, numerators are 109,105
Denominators are 65,2112
The GCF of 109,105 is 1 .
LCM of 65,2112 is 137280.
The greatest common factor of 109/65,105/2112 = [GCF of 109,105]/[LCM of 65,2112]= 1/137280
Therefore, the GCF of 109/65,105/2112 is 1/137280.
To find the highest common factor of 109,105, 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 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 109,105 is 1.
Lets's calculate GCF of 109,105
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 109,105 By Matching Biggest Common Factor Method
Now, list down the factors of 109
:1,109
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 109,105 . The biggest common factor number is the GCF number.
So the greatest common factor 109,105 is 1.
Lets's calculate LCM of 65,2112
Given numbers has no common factors except 1. So, there LCM is their product i.e 137280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/137280
Therefore, the GCF of Fractions 109/65,105/2112 is 1/137280
Least Common Multiple of 65,2112 with GCF Formula
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 65,2112 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,2112) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(65,2112) x common factors =1 x 1 = 1
LCM(65,2112) = ( 65 × 2112 ) / 1
LCM(65,2112) = 137280 / 1
LCM(65,2112) = 137280
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FAQs on GCF of Fractions of 109/65, 105/2112
1. What is the HCF of 109,105?
The HCF of 109,105 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 109/65, 105/2112?
Answer: GCF of Numerators as per given numbers 109/65, 105/2112 is
GCF of Numerators i.e. for 109,105 is 1
LCM of denominators i.e. for 65,2112 is 137280.
Thus, GCF of Fractions is 1/137280.Finally, GCF of Fractions for 109/65, 105/2112 is 1/137280.