[Math] Proving that a number has at least 3 distinct prime factors.

Question

Let abc be a 3-digit natural number (written in base 10). Prove that the 6-digit number abcabc has at least three distinct prime factors.

I know that to prove that the 6-digit number has at least three distinct prime factors, it suffices to show that abc has three distinct prime factors. However, the example that my teacher gave me was this,

Since abcabc = 1001·abc, it suffices to show that 1001 has three distinct prime factors. In fact, 1001 = 7·11·13

I seem to misunderstand the concept of a 3-digit number written in base 10. As far as I know, the base 10 system is the 0-9 numbering system. If so, then how can a 3-digit natural number be 1001? What have I misunderstood here?

Answer 1

It is a simple calculuation. $1001 \times abc = 1000 \times abc + abc = abcabc$.