To determine how many prime numbers exist between 21 and 35, we first need to understand what a prime number is. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In simpler terms, a prime number has exactly two distinct divisors: 1 and itself.
Let’s examine the numbers between 21 and 35: 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, and 35. Now, we’ll check each of these numbers to see if they are prime:
- 22: Divisible by 1, 2, 11, 22 (not prime)
- 23: Divisible only by 1 and 23 (prime)
- 24: Divisible by 1, 2, 3, 4, 6, 8, 12, 24 (not prime)
- 25: Divisible by 1, 5, 25 (not prime)
- 26: Divisible by 1, 2, 13, 26 (not prime)
- 27: Divisible by 1, 3, 9, 27 (not prime)
- 28: Divisible by 1, 2, 4, 7, 14, 28 (not prime)
- 29: Divisible only by 1 and 29 (prime)
- 30: Divisible by 1, 2, 3, 5, 6, 10, 15, 30 (not prime)
- 31: Divisible only by 1 and 31 (prime)
- 32: Divisible by 1, 2, 4, 8, 16, 32 (not prime)
- 33: Divisible by 1, 3, 11, 33 (not prime)
- 34: Divisible by 1, 2, 17, 34 (not prime)
- 35: Divisible by 1, 5, 7, 35 (not prime)
From this examination, we find that the prime numbers between 21 and 35 are:
- 23
- 29
- 31
Therefore, there are a total of three prime numbers between 21 and 35.