Introduction:
In this question, we need to determine the number of numbers less than 1024 which are prime to 1024. To solve this problem, we will break it down into smaller steps and analyze each step in detail.

Step 1: Prime Factorization of 1024:
To find the numbers that are prime to 1024, we first need to understand the prime factorization of 1024. Prime factorization is the process of expressing a number as the product of its prime factors. The prime factorization of 1024 can be written as:

1024 = 2^10

So, 1024 has a single prime factor, which is 2 raised to the power of 10.

Step 2: Prime Numbers:
Next, we need to understand what prime numbers are. Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. In other words, prime numbers are numbers that cannot be divided evenly by any other number except 1 and itself.

Step 3: Numbers Prime to 1024:
To find the numbers that are prime to 1024, we need to find the numbers that do not have 2 as a factor. Since 1024 has only one prime factor, which is 2 raised to the power of 10, any number that is not divisible by 2 will be prime to 1024.

Step 4: All Prime Numbers less than 1024:
All prime numbers less than 1024 are prime to 1024 because they do not have 2 as a factor. To determine the number of prime numbers less than 1024, we can use various methods such as sieving or checking divisibility by all numbers less than the square root of 1024.

Answer:
Therefore, the correct answer is option D, which states that all prime numbers less than 1024 are prime to 1024. This is because prime numbers do not have 2 as a factor, and since 1024 only has 2 as a prime factor, all prime numbers less than 1024 will not be divisible by 2 and hence prime to 1024.

There are 512 positive integers (less than 1,024) that are coprime with 1,024. And there are approximately 174 prime numbers less than or equal to 1,024.