In natural numbers less than 1000, how many even divisors are there?

In natural numbers less than 1000, how many even divisors are there?

How many even divisors are there in less than 1000 natural numbers?
Answer: 999-31 = 968
Idea: except for 1 and itself, other divisors of natural numbers are basically corresponding, so under normal circumstances, they are even divisors. In special cases, they are the square of natural numbers. Because the corresponding divisor is itself, the number has odd divisors. For example, the divisors of 12 have 1, 12; 2, 6; 3, 4; 6 divisors, three groups. The divisors of 9 have 1, 9; 3, Count 3 divisors, and repeat the divisors of the second group
To sum up, 31 square numbers (1,4,9,...) are removed from the natural numbers less than 1000 Other natural numbers contain even divisors

What is the minimum natural number with only 20 divisors? What is the sum of these 20 divisors
The explanation is easy to understand and has formulas

The number of divisors of a composite number is the continuous product of the exponents of each prime factor plus 1 after strictly decomposing the prime factors. This problem is based on this inverse operation. Since it is to find the minimum number, the prime factors should be 2, 3, 5, 7, 9 Because, decomposition prime factor 20 = 2 * 2 * 5 = 4 * 5 = 2 * 10, so, only 20 divisors have 4

There are 20 positive divisors of the minimum natural number is 240, why? To answer the process in detail

Any natural number, 1 and itself must be its positive divisor. We need to find another 18 divisors between them If we want to find the smallest natural number with 20 positive divisors, we should start from the smallest one (without considering the divisor 1 and itself): first, we should look at 2, there is a divisor; if there are two divisors, then