8.1. Find all three-digit numbers divisible by 4, in which the ratio of the first digit to the second is equal to the ratio of the second digit to the third.
Answer: $124,248,444,888,964$.

Solution. Let the desired number be $n=\overline{a b c}$. From the condition, it follows that the square of the middle digit is equal to the product of the extreme digits, and the last digit is even. From this, it immediately follows that the middle digit is also even. Let's consider the possible middle digits and find all factorizations of their squares into suitable products $b^{2}=a \cdot c$, the factors of which do not exceed 9.

1) $b=2, b^{2}=4=1 \cdot 4=2 \cdot 2=4 \cdot 1$. The first factorization gives the suitable number 124, the second and third do not divide by 4.
2) $b=4, b^{2}=16=2 \cdot 8=4 \cdot 4=8 \cdot 2$. The first two factorizations give the suitable numbers 248 and 444, the last one does not divide by 4.
3) $b=6, b^{2}=36=4 \cdot 9=6 \cdot 6=9 \cdot 4$. The third factorization gives the suitable number 964, the first and second do not divide by 4.
4) $b=8, b^{2}=64=8 \cdot 8$, we get the suitable number 888.