# Composite Cat Cannot divide its immediate lower neighbors factorial without leaving a remainder

Find this unique composite cat given the information in this title.

Four

Reason

$$\frac{3!}{4} = \frac{6}{4} = 1 + \frac{1}{2}$$ leaves a remainder

Hint from question

cat - may be four legs

Uniqueness

2 is the only even prime number. Before 4 , 2 occurs only once and 4 is a multiple of 2. And 3! = 6 = 3.2.1 has only one 2, hence it leaves a remainder.  Whereas for other composite numbers say, $$n$$, $$(n-1)!$$ has all the factors of $$n$$, and thus doesn't leave a remainder.

• I mean, rot13(guerr yrnirf n erznvaqre jura qvivqvat gjb snpgbevny)....? – El-Guest May 15 '19 at 19:29
• @El-Guest "Composite" cat. – hexomino May 15 '19 at 21:41
• @hexomino by now you should know I don’t know how to read – El-Guest May 15 '19 at 21:42