GCF of 162/17, 945/340
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 162/17, 945/340 i.e 27/340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 162/17, 945/340.
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 162/17,945/340?
Given fractions are 162/17,945/340
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 162/17,945/340, numerators are 162,945
Denominators are 17,340
The GCF of 162,945 is 27 .
LCM of 17,340 is 340.
The greatest common factor of 162/17,945/340 = [GCF of 162,945]/[LCM of 17,340]= 27/340
Therefore, the GCF of 162/17,945/340 is 27/340.
To find the highest common factor of 162,945, we have to find the factors of both numbers and list the highest common factor.
The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162
The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945
The HCF of 162,945 is 27.
Lets's calculate GCF of 162,945
| 3 | 162, 945 |
| 3 | 54, 315 |
| 3 | 18, 105 |
| 6, 35 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Greatest Common Factor of 162,945 By Matching Biggest Common Factor Method
Now, list down the factors of 162
:1,2,3,6,9,18,27,54,81,162
Now, list down the factors of 945
:1,3,5,7,9,15,21,27,35,45,63,105,135,189,315,945
Greatest Common Factor
We found the factors 162,945 . The biggest common factor number is the GCF number.
So the greatest common factor 162,945 is 27.
Lets's calculate LCM of 17,340
| 17 | 17, 340 |
| 1, 20 |
∴ So the LCM of the given numbers is 17 x 1 x 20 = 340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/340
Therefore, the GCF of Fractions 162/17,945/340 is 27/340
Least Common Multiple of 17,340 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 17,340 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,340) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(17,340) x common factors =17 x 1 = 17
LCM(17,340) = ( 17 × 340 ) / 17
LCM(17,340) = 5780 / 17
LCM(17,340) = 340
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FAQs on GCF of Fractions of 162/17, 945/340
1. What is the HCF of 162,945?
The HCF of 162,945 is 27
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 162/17, 945/340?
Answer: GCF of Numerators as per given numbers 162/17, 945/340 is
GCF of Numerators i.e. for 162,945 is 27
LCM of denominators i.e. for 17,340 is 340.
Thus, GCF of Fractions is 27/340.Finally, GCF of Fractions for 162/17, 945/340 is 27/340.