GCF of 216/107, 189/205
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 216/107, 189/205 i.e 27/21935 easily. The following is the detailed procedure to determine the greatest common factor of fractions 216/107, 189/205.
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 216/107,189/205?
Given fractions are 216/107,189/205
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 216/107,189/205, numerators are 216,189
Denominators are 107,205
The GCF of 216,189 is 27 .
LCM of 107,205 is 21935.
The greatest common factor of 216/107,189/205 = [GCF of 216,189]/[LCM of 107,205]= 27/21935
Therefore, the GCF of 216/107,189/205 is 27/21935.
To find the highest common factor of 216,189, we have to find the factors of both numbers and list the highest common factor.
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The HCF of 216,189 is 27.
Lets's calculate GCF of 216,189
| 3 | 216, 189 |
| 3 | 72, 63 |
| 3 | 24, 21 |
| 8, 7 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Greatest Common Factor of 216,189 By Matching Biggest Common Factor Method
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Greatest Common Factor
We found the factors 216,189 . The biggest common factor number is the GCF number.
So the greatest common factor 216,189 is 27.
Lets's calculate LCM of 107,205
Given numbers has no common factors except 1. So, there LCM is their product i.e 21935
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/21935
Therefore, the GCF of Fractions 216/107,189/205 is 27/21935
Least Common Multiple of 107,205 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 107,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(107,205) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(107,205) x common factors =1 x 1 = 1
LCM(107,205) = ( 107 × 205 ) / 1
LCM(107,205) = 21935 / 1
LCM(107,205) = 21935
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FAQs on GCF of Fractions of 216/107, 189/205
1. What is the HCF of 216,189?
The HCF of 216,189 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 216/107, 189/205?
Answer: GCF of Numerators as per given numbers 216/107, 189/205 is
GCF of Numerators i.e. for 216,189 is 27
LCM of denominators i.e. for 107,205 is 21935.
Thus, GCF of Fractions is 27/21935.Finally, GCF of Fractions for 216/107, 189/205 is 27/21935.