G7.2 A six-digit figure 111aaa is the product of two consecutive positive integers $b$ and $b+1$, find the value of $b$.
Reference: $\mathbf{2 0 0 1}$ FG2.3 Given that $111111222222=c \times(c+1)$
$$
111222=111000+222=111 \times 1000+2 \times 111=111 \times 1002=111 \times 3 \times 334=333 \times 334 ; b=333
$$