To determine which of the given numbers is not a prime number, let's carefully analyze the characteristics of each number:
1. Definition of a Prime Number:
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number must be divisible only by 1 and the number itself.
2. Options Analysis:
- 17:
- Divisors of 17: 1, 17
- Since it has no other divisors, it is a prime number.
- 23:
- Divisors of 23: 1, 23
- Since it has no other divisors, it is a prime number.
- 31:
- Divisors of 31: 1, 31
- Since it has no other divisors, it is a prime number.
- 51:
- Let's check divisors of 51:
- 51 divided by 1 is 51
- 51 divided by 3 is 17 (since 51 = 3 17)
- 51 divided by 17 is 3 (since 51 = 3 17)
- 51 divided by 51 is 1
- Since 51 can be divided by numbers other than 1 and 51, it is not a prime number.
3. Conclusion:
Among the given numbers, all the numbers 17, 23, and 31 are prime because they only have 1 and themselves as divisors. However, 51 is not a prime number because it has additional divisors (3 and 17).
Therefore, the answer is:
D 51
This is not a prime number.
