GCF of 69/23, 81/55, 21/111
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 69/23, 81/55, 21/111 i.e 3/140415 easily. The following is the detailed procedure to determine the greatest common factor of fractions 69/23, 81/55, 21/111.
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 69/23,81/55,21/111?
Given fractions are 69/23,81/55,21/111
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 69/23,81/55,21/111, numerators are 69,81,21
Denominators are 23,55,111
The GCF of 69,81,21 is 3 .
LCM of 23,55,111 is 140415.
The greatest common factor of 69/23,81/55,21/111 = [GCF of 69,81,21]/[LCM of 23,55,111]= 3/140415
Therefore, the GCF of 69/23,81/55,21/111 is 3/140415.
To find the highest common factor of 69,81,21, we have to find the factors of both numbers and list the highest common factor.
The factors of 69 are 1, 3, 23, 69
The factors of 81 are 1, 3, 9, 27, 81
The factors of 21 are 1, 3, 7, 21
The HCF of 69,81,21 is 3.
Lets's calculate GCF of 69,81,21
| 3 | 69, 81, 21 |
| 23, 27, 7 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 69,81,21 By Matching Biggest Common Factor Method
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 81
:1,3,9,27,81
Now, list down the factors of 21
:1,3,7,21
Greatest Common Factor
We found the factors 69,81,21 . The biggest common factor number is the GCF number.
So the greatest common factor 69,81,21 is 3.
Lets's calculate LCM of 23,55,111
Given numbers has no common factors except 1. So, there LCM is their product i.e 140415
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/140415
Therefore, the GCF of Fractions 69/23,81/55,21/111 is 3/140415
Least Common Multiple of 23,55,111 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 23,55,111 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(23,55,111) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(23,55,111) x common factors =1 x 1 = 1
LCM(23,55,111) = ( 23 × 55 × 111 ) / 1
LCM(23,55,111) = 140415 / 1
LCM(23,55,111) = 140415
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FAQs on GCF of Fractions of 69/23, 81/55, 21/111
1. What is the HCF of 69,81,21?
The HCF of 69,81,21 is 3
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 69/23, 81/55, 21/111?
Answer: GCF of Numerators as per given numbers 69/23, 81/55, 21/111 is
GCF of Numerators i.e. for 69,81,21 is 3
LCM of denominators i.e. for 23,55,111 is 140415.
Thus, GCF of Fractions is 3/140415.Finally, GCF of Fractions for 69/23, 81/55, 21/111 is 3/140415.