How many of the divisors of 1800 are multiples of 12?

Every such divisor can be written as 12m, and 12m divides 1800 exactly when m divides 1800 ÷ 12 = 150. Since $150=2\times 3\times 5^2$, it has $2\times 2\times 3=12$ divisors, and each gives a different answer: 12, 24, 36, 60, 72, 120, 180, 300, 360, 600, 900 and 1800. The trap 36 is the TOTAL number of divisors of $1800=2^3\times 3^2\times 5^2$, namely $4\times 3\times 3$. Reading the question as 'multiples of 6' gives $1800÷6=300=2^2\times 3\times 5^2$ with 18 divisors. And writing 150 as $2\times 3\times 5$ — losing the second 5 — leaves only 8.