Hey there! Understanding prime numbers can be exciting, just like solving a fun puzzle! Let's start with what a prime number is. A prime number is a whole number greater than 1 that has only two positive divisors: 1 and itself. This means it can only be divided evenly by 1 and the number itself, with no remainder.
Let's find the prime numbers up to 100 together. We'll start with the number 2, which is the first prime number. Then we'll use a simple method called the 'Sieve of Eratosthenes' to find the remaining prime numbers.
We'll make a list of numbers from 1 to 100 and start crossing out the multiples of each prime number as we find them. For example, when we come to the number 2, we'll circle it as a prime number and then cross out all its multiples - 4, 6, 8, 10, and so on. We'll continue this process for each remaining uncircled number, marking the primes and crossing out their multiples.
Here's a little example to make it clearer: We start with the number 2 as our first prime. Then we'll cross out its multiples: 4, 6, 8, 10, 12, and so on. Next, we find the next uncrossed number, which is 3, and circle it as a prime. We then cross out its multiples. We continue this process until we reach the end of our list. The numbers that remain uncrossed at the end are the prime numbers up to 100!
So, using this method, we find that the prime numbers up to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.