Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. To find the prime numbers between 25 and 50, we will check each number in that range to see if it has only two distinct positive divisors.
Starting from 26 to 49, we review the numbers:
- 26: Divisible by 2 and 13
- 27: Divisible by 3 and 9
- 28: Divisible by 2 and 14
- 29: Only divisible by 1 and 29 (prime)
- 30: Divisible by 2, 3, 5, 6, 10, and 15
- 31: Only divisible by 1 and 31 (prime)
- 32: Divisible by 2 and 16
- 33: Divisible by 3 and 11
- 34: Divisible by 2 and 17
- 35: Divisible by 5 and 7
- 36: Divisible by 2, 3, 4, 6, 9, 12, and 18
- 37: Only divisible by 1 and 37 (prime)
- 38: Divisible by 2 and 19
- 39: Divisible by 3 and 13
- 40: Divisible by 2, 4, 5, 8, 10, 20
- 41: Only divisible by 1 and 41 (prime)
- 42: Divisible by 2, 3, 6, 7, 14, and 21
- 43: Only divisible by 1 and 43 (prime)
- 44: Divisible by 2, 4, 11, and 22
- 45: Divisible by 3, 5, 9, and 15
- 46: Divisible by 2 and 23
- 47: Only divisible by 1 and 47 (prime)
- 48: Divisible by 2, 3, 4, 6, 8, 12, 16, and 24
- 49: Divisible by 7
Thus, the prime numbers between 25 and 50 are:
- 29
- 31
- 37
- 41
- 43
- 47