GCF of 135/206, 182/218
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 135/206, 182/218 i.e 1/22454 easily. The following is the detailed procedure to determine the greatest common factor of fractions 135/206, 182/218.
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 135/206,182/218?
Given fractions are 135/206,182/218
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 135/206,182/218, numerators are 135,182
Denominators are 206,218
The GCF of 135,182 is 1 .
LCM of 206,218 is 22454.
The greatest common factor of 135/206,182/218 = [GCF of 135,182]/[LCM of 206,218]= 1/22454
Therefore, the GCF of 135/206,182/218 is 1/22454.
To find the highest common factor of 135,182, we have to find the factors of both numbers and list the highest common factor.
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135
The factors of 182 are 1, 2, 7, 13, 14, 26, 91, 182
The HCF of 135,182 is 1.
Lets's calculate GCF of 135,182
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 135,182 By Matching Biggest Common Factor Method
Now, list down the factors of 135
:1,3,5,9,15,27,45,135
Now, list down the factors of 182
:1,2,7,13,14,26,91,182
Greatest Common Factor
We found the factors 135,182 . The biggest common factor number is the GCF number.
So the greatest common factor 135,182 is 1.
Lets's calculate LCM of 206,218
| 2 | 206, 218 |
| 103, 109 |
∴ So the LCM of the given numbers is 2 x 103 x 109 = 22454
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/22454
Therefore, the GCF of Fractions 135/206,182/218 is 1/22454
Least Common Multiple of 206,218 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 206,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(206,218) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(206,218) x common factors =2 x 1 = 2
LCM(206,218) = ( 206 × 218 ) / 2
LCM(206,218) = 44908 / 2
LCM(206,218) = 22454
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FAQs on GCF of Fractions of 135/206, 182/218
1. What is the HCF of 135,182?
The HCF of 135,182 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 135/206, 182/218?
Answer: GCF of Numerators as per given numbers 135/206, 182/218 is
GCF of Numerators i.e. for 135,182 is 1
LCM of denominators i.e. for 206,218 is 22454.
Thus, GCF of Fractions is 1/22454.Finally, GCF of Fractions for 135/206, 182/218 is 1/22454.