GCF of 55/23, 20/31, 68/82, 38/34
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 55/23, 20/31, 68/82, 38/34 i.e 1/993922 easily. The following is the detailed procedure to determine the greatest common factor of fractions 55/23, 20/31, 68/82, 38/34.
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 55/23,20/31,68/82,38/34?
Given fractions are 55/23,20/31,68/82,38/34
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 55/23,20/31,68/82,38/34, numerators are 55,20,68,38
Denominators are 23,31,82,34
The GCF of 55,20,68,38 is 1 .
LCM of 23,31,82,34 is 993922.
The greatest common factor of 55/23,20/31,68/82,38/34 = [GCF of 55,20,68,38]/[LCM of 23,31,82,34]= 1/993922
Therefore, the GCF of 55/23,20/31,68/82,38/34 is 1/993922.
To find the highest common factor of 55,20,68,38, we have to find the factors of both numbers and list the highest common factor.
The factors of 55 are 1, 5, 11, 55
The factors of 20 are 1, 2, 4, 5, 10, 20
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 38 are 1, 2, 19, 38
The HCF of 55,20,68,38 is 1.
Lets's calculate GCF of 55,20,68,38
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 55,20,68,38 By Matching Biggest Common Factor Method
Now, list down the factors of 55
:1,5,11,55
Now, list down the factors of 20
:1,2,4,5,10,20
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 38
:1,2,19,38
Greatest Common Factor
We found the factors 55,20,68,38 . The biggest common factor number is the GCF number.
So the greatest common factor 55,20,68,38 is 1.
Lets's calculate LCM of 23,31,82,34
| 2 | 23, 31, 82, 34 |
| 23, 31, 41, 17 |
∴ So the LCM of the given numbers is 2 x 23 x 31 x 41 x 17 = 993922
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/993922
Therefore, the GCF of Fractions 55/23,20/31,68/82,38/34 is 1/993922
Least Common Multiple of 23,31,82,34 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 23,31,82,34 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(23,31,82,34) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(23,31,82,34) x common factors =1 x 2 = 2
LCM(23,31,82,34) = ( 23 × 31 × 82 × 34 ) / 2
LCM(23,31,82,34) = 1987844 / 2
LCM(23,31,82,34) = 993922
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 55/23, 20/31, 68/82, 38/34
1. What is the HCF of 55,20,68,38?
The HCF of 55,20,68,38 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 55/23, 20/31, 68/82, 38/34?
Answer: GCF of Numerators as per given numbers 55/23, 20/31, 68/82, 38/34 is
GCF of Numerators i.e. for 55,20,68,38 is 1
LCM of denominators i.e. for 23,31,82,34 is 993922.
Thus, GCF of Fractions is 1/993922.Finally, GCF of Fractions for 55/23, 20/31, 68/82, 38/34 is 1/993922.