### A note on the Factorial Function

### Write down 0,1,2,3,4,5 and put parallel **square** of each number like 0,1,4,9,16,25, then start to subtract the bigger one to the lower one (1–0),(4–1),(9–4),(16–9) and (25–16) to get 1,3,5,7,9 and again subtract the bigger one to the lower one (3–1),(5–3),(7–5) and (9–7) to get **(2,2,2,2)**.

Again we

**squared each number**, at the same time we**cubed each number**(0,1,8,27,64,125,216) and the same procedure follows, subtract the bigger one to the lower one (1–0),(8–1),(27–8),(64–27) ,(125–64) and(216–125) to get (1,7,19,37,61,91) and again (7–1),(19–7),(37–19),(61–37) and (91–61), to get (6,12,18,24,30) same again(12–6),(18–12),24–18) and (30–24)**till the result come out**here we get (**6,6,6,6)**.At the same time if we do it again for 4 and 5 (power).When we get

**2 for 2 ,6 for 3 ,24 for 4 and 120 for 5. The result is the factorial function.**