A natural number has 10 different divisors, but its prime factor is only 3 and 5. What is the maximum natural number satisfying these conditions? Urgent! 1

A natural number has 10 different divisors, but its prime factor is only 3 and 5. What is the maximum natural number satisfying these conditions? Urgent! 1

Because the prime factor is only 3 and 5, the divisor has 1 and itself, 3 and 5, and the rest is composed of the product of 3 and 5, which is analyzed as 3 * 5
3*5*5
3*5*5*5
5*5
5*5*5
5*5*5*5
So this number is 3 * 5 * 5 * 5 * 5 = 1875

There is a natural number, which has 3 different prime factors and 12 divisors. What is the minimum of this natural number?

The minimum natural number is 60
60 has three different quality factors: 2, 3 and 5,
There are 12 divisors 1,2,3,4,5,6,10,12,15,20,30,60

There is a natural number with 10 different divisors, but there are only two kinds of prime factors: 2 and 3
To have a detailed problem-solving steps and instructions

Let this natural number be 2 ^ m × 3 ^ n
Then the number of divisors is (M + 1) × (n + 1)
So m and N are one and four
In order to make the natural number larger, let the power of 3 be more
That is, 2 × 3 ^ 4 = 162