Question 13
We say that a positive three-digit integer is three stars if it is the result of the product of three distinct prime numbers. For example, $286=2 \cdot 11 \cdot 13$ is a three-star number, but $30=2 \cdot 3 \cdot 5$ and $275=5 \cdot 5 \cdot 13$ are not three-star numbers, as the first only has two digits and the second is not the product of three distinct primes.
a) What is the smallest number three stars?
b) Shows that each number three stars has a common divider with $30$ greater than $1$.
a) What is the smallest number three stars?
b) Shows that each number three stars has a common divider with $30$ greater than $1$.