The correct answer is (a) 25.
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number.
The first 25 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, and 83.
To find the prime numbers between 1 and 100, we can start by listing all the natural numbers from 2 to 100. Then, we can eliminate any number that is divisible by any of the prime numbers we have already found. For example, we can eliminate 6 because it is divisible by 2. We can also eliminate 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, and 90 because they are all divisible by 2.
After we have eliminated all the composite numbers, we are left with the following prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, and 83. This gives us a total of 25 prime numbers between 1 and 100.
The other options are incorrect because they do not represent the correct number of prime numbers between 1 and 100.