Factors of 
44 = 2*2*11
180 = 2*2*3*3*5

HCF of 44 and 180
= 2*2
= 4

Then, 
13m - 3 = 4
13m = 7
m = 7/13

Value of m = 7/13 @ns..

Problem: Find the value of m if the HCF of two numbers is 44 and 180 is expressed in the form of 13m-3.

Solution:
To solve this problem, we can use the formula:
HCF × LCM = product of two numbers

Step 1: Find the LCM of the two numbers
Let x and y be the two numbers.
Product of two numbers = xy
HCF of two numbers = 44
LCM × HCF = xy
LCM × 44 = xy

We need to find the LCM of x and y.
We can factorize 44 as 2 × 2 × 11.
Let's factorize x and y into their prime factors and then find their LCM.

Prime factorization of 180 = 2 × 2 × 3 × 3 × 5
Prime factorization of xy = 2 × 2 × 11 × p × q

To find the LCM, we need to take the highest power of each prime factor. So, the LCM is:
LCM = 2 × 2 × 3 × 3 × 5 × 11 × p × q
LCM = 2^2 × 3^2 × 5 × 11 × pq
LCM = 2^2 × 3^2 × 5 × 11 × (13m - 3) (Substituting xy with 13m - 3)

Step 2: Substitute LCM value in the formula
Now, we can substitute the LCM value in the formula:
LCM × HCF = xy
(2^2 × 3^2 × 5 × 11 × (13m - 3)) × 44 = xy

Simplifying the above equation, we get:
2^3 × 3^2 × 5 × 11 × (13m - 3) = xy

Substituting the value of xy as 180 × 44, we get:
2^3 × 3^2 × 5 × 11 × (13m - 3) = 180 × 44

Simplifying the above equation, we get:
39m = 189

Therefore, the value of m is:
m = 189/39 = 5

Answer: The value of m is 5.