Find the rest

-The prime factorization of a number with exactly $15$ positive divisors is $a ^ 2 \times b ^ 4$ or $c ^ {\text {14}}$ with $a; b; c$ prime numbers because the $+ 1$ exponent product must be $15$ and the only $15$ factoring is: $3 \times 5 and 1 \times 15$ .

-The fact that this number is a multiple of $15$ implies that the prime factors component $15$ , namely $3$ and $5$ , also make up this number. Hence the only corresponding numbers are $3 ^ 2 \times 5 ^ 4 = 5625$ and $3 ^ 4 \times 5 ^ 2 = 2025$ .