# Find the last digit of (K)

#### idontknow

Find the last digit of natural number $$\displaystyle (K)$$ if
$$\displaystyle K=n 11^n$$ ; $$\displaystyle n \in N$$

#### v8archie

Math Team
It's the last digit of $n$, quite trivially.

#### idontknow

Let $$\displaystyle \ell{\{T\}}$$ be the last digit of $$\displaystyle T$$
$$\displaystyle \ell{\{K\}}=\ell{\{n11^{n}\}}=\ell{\{n\}}\ell{\{11^n\}}$$
$$\displaystyle \ell{\{K\}}=\ell{\{n\}}=n-10int(\frac{n}{10})=10frac{\{\frac{n}{10}\}}$$ ;; frac means fractional part

#### v8archie

Math Team
It's significantly cleaner to work modulo 10.