Without actual division, show that 11 is a factor of 1,10,011.

Here 1,10,011 = 1,10,000 + 11

= 11 × 10,000 + 11 × 1

= 11 × (10,000 + 1)

= 11 × 10,001

It is clear that 11 is a factor of 11 × 10,001.