I am looking for an idea on how to decipher a columnar transposition cipher without knowing the key or the length of the key.

When I take the cipher text as input to my algorithm I will guess the length of the key to be the factors of the length of the cipher text.

I will take the first factor suppose the length was 20 letters so I will take 2*10 (2 rows and 10 columns). Now I want to arrange the cipher text in the columns and read it row wise to see if there is any word forming and match it with a dictionary if it is something sensible. If it matches the dictionary then it means it is in correct order or else I want to know how to make other combinations of the columns and read the string again row wise.

Please suggest another approach that is more efficient.