GCF of 116/302, 405/204
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 116/302, 405/204 i.e 1/30804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 116/302, 405/204.
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 116/302,405/204?
Given fractions are 116/302,405/204
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 116/302,405/204, numerators are 116,405
Denominators are 302,204
The GCF of 116,405 is 1 .
LCM of 302,204 is 30804.
The greatest common factor of 116/302,405/204 = [GCF of 116,405]/[LCM of 302,204]= 1/30804
Therefore, the GCF of 116/302,405/204 is 1/30804.
To find the highest common factor of 116,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 116 are 1, 2, 4, 29, 58, 116
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 116,405 is 1.
Lets's calculate GCF of 116,405
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 116,405 By Matching Biggest Common Factor Method
Now, list down the factors of 116
:1,2,4,29,58,116
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 116,405 . The biggest common factor number is the GCF number.
So the greatest common factor 116,405 is 1.
Lets's calculate LCM of 302,204
| 2 | 302, 204 |
| 151, 102 |
∴ So the LCM of the given numbers is 2 x 151 x 102 = 30804
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30804
Therefore, the GCF of Fractions 116/302,405/204 is 1/30804
Least Common Multiple of 302,204 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 302,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(302,204) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(302,204) x common factors =2 x 1 = 2
LCM(302,204) = ( 302 × 204 ) / 2
LCM(302,204) = 61608 / 2
LCM(302,204) = 30804
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FAQs on GCF of Fractions of 116/302, 405/204
1. What is the HCF of 116,405?
The HCF of 116,405 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 116/302, 405/204?
Answer: GCF of Numerators as per given numbers 116/302, 405/204 is
GCF of Numerators i.e. for 116,405 is 1
LCM of denominators i.e. for 302,204 is 30804.
Thus, GCF of Fractions is 1/30804.Finally, GCF of Fractions for 116/302, 405/204 is 1/30804.