# Recursive Digit Sums

**Number Theory**Level 3

Let \(A\) be a number with 2001 digits such that \(A\) is a multiple of \(10!\) Let \(B\) be the digit sum of \(A\), \(C\) be the digit sum of \(B\), and \(D\) be the digit sum of \(C\). What is the **unit’s digit** of \(D\)?

**Details and assumptions**

The **digit sum** of a number is the sum of all its digits. For example the digit sum of 1123 is \(1 + 1 + 2 + 3 = 7\).