Among the 100 natural numbers from 1 to 100, how many numbers have no divisor 3 and cannot be divisible by 7?

1--100,
If there is a divisor 3, there are 100 / 3 = 33
100 / 7 = 14 can be divided by 7
That is, there are 3 divisors and 100 / 21 = 4 divisors by 7
So the numbers that have no divisor 3 and cannot be divided by 7 are as follows:
100-33-14 + 4 = 57

Find a natural number that can be divided by 30 and has exactly 30 divisors

720
one thousand and two hundred
one thousand six hundred and twenty
four thousand and fifty
seven thousand and five hundred
eleven thousand two hundred and fifty

It is known that a = {natural number divisible by 2}, B = {natural number divisible by 4}. What kind of set does a ∪ B and a ∩ B represent?

The natural number divisible by 2 can be expressed as 2n, n ∈ n
The natural number divisible by 4 can be expressed as 4N, n ∈ n
∴A∪B=A=｛x|x=2n,n∈N｝
A∩B=B=｛x|x=4n,n∈N｝

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