Consider the numbers 13, 16, 27 and 41.
A. Which of these numbers are prime? How do you know?
B. Which of these numbers are composite? How do you know?
A. Out of the given numbers, the number 41 is prime. A prime number is a number that is greater than 1 and can only be divided evenly by 1 and itself. To determine if a number is prime, we can check for divisibility by all numbers less than or equal to the square root of the number. In the case of 41, we check divisibility by numbers up to 6 (since √41 is approximately 6.4) and find that 41 is not divisible by any of them, thus confirming it as a prime number.
B. The numbers 13, 16, and 27 are composite. A composite number is a positive integer greater than 1 that is not prime and can be divided evenly by at least one other number besides 1 and itself.
The number 13 is prime (as discussed in part A), so it is not composite.
The number 16 is composite because it can be divided evenly by numbers other than 1 and itself, such as 2, 4, and 8.
The number 27 is also composite because it can be divided evenly by numbers other than 1 and itself, such as 3 and 9.