Which of the following numbers are prime numbers? Select ALL that apply.
23 and 29 are prime numbers.
Prime numbers are defined as natural numbers greater than 1 that have no positive divisors other than 1 and themselves. Among the given options, 23 and 29 meet this criterion, as they cannot be evenly divided by any other numbers besides 1 and themselves.
21 is not a prime number because it can be divided evenly by 1, 3, 7, and 21. Specifically, it can be expressed as the product of 3 and 7, indicating that it has divisors other than 1 and itself.
23 is a prime number since it has no divisors other than 1 and 23. It cannot be divided evenly by any other integers, confirming its status as a prime.
25 is not a prime number because it can be expressed as 5 multiplied by 5 (5 x 5 = 25). This means it has divisors other than 1 and itself, specifically 5.
27 is not a prime number as it can be divided evenly by 1, 3, 9, and 27. It can also be expressed as 3 multiplied by 9, which means it has factors other than 1 and itself.
29 is a prime number since it is only divisible by 1 and 29. There are no other integers that can divide 29 evenly, affirming its classification as a prime number.
In summary, the only prime numbers among the options provided are 23 and 29, as both possess no divisors other than 1 and themselves. The other numbers, 21, 25, and 27, are composite, having divisors beyond just 1 and their own values. Understanding prime numbers is fundamental in various mathematical applications, including number theory and cryptography.
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