To identify which number is a prime number among the given options: 65, 90, 56, and 53, we need to understand what defines a prime number. A prime number is a natural number greater than 1 that has no other divisors other than 1 and itself. In other words, it can only be divided by 1 and itself without leaving a remainder.
### Step-by-Step Solution:
1. Check 65:
- 65 is divided by 1 and 65 (trivially).
- 65 can be divided by 5 (since it ends in 5), giving us 65 ÷ 5 = 13.
- Therefore, 65 has divisors other than 1 and itself (for example, 5 and 13).
- 65 is not a prime number.
2. Check 90:
- 90 is divided by 1 and 90 (trivially).
- 90 is an even number (ends in 0), so it can be divided by 2, resulting in 90 ÷ 2 = 45.
- Additionally, 90 can be divided by multiple other numbers such as 3, 5, 6, 9, 10, 15, etc.
- Therefore, 90 has multiple divisors other than 1 and itself.
- 90 is not a prime number.
3. Check 56:
- 56 is divided by 1 and 56 (trivially).
- 56 is an even number (ends in 6), so it can be divided by 2, giving us 56 ÷ 2 = 28.
- Additionally, 56 can be divided by 4, 7, 8, and other numbers.
- Therefore, 56 has multiple divisors other than 1 and itself.
- 56 is not a prime number.
4. Check 53:
- 53 is divided by 1 and 53 (trivially).
- 53 is not divisible by 2 (since it is odd), nor by 3 (5+3=8 which is not divisible by 3), nor by 5 (it does not end in 0 or 5).
- We can continue testing with higher prime numbers (7, 11, etc.) but we see that 53 does not evenly divide by any of these.
- Therefore, 53 has no divisors other than 1 and itself.
- 53 is a prime number.
### Conclusion:
Among the numbers 65, 90, 56, and 53, the number that is a prime number is:
D. 53.
