Question

2, 47, 79, 38, 22, 65
prime numbers
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composite numbers
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Explanation:

Step1: Define Prime and Composite Numbers

A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. A composite number is a positive integer that has at least one positive divisor other than 1 and itself.

Step2: Analyze Each Number

• For 2: It is greater than 1 and its only divisors are 1 and 2. So, 2 is prime.
• For 47: It is greater than 1. We check divisors from 2 to $\sqrt{47}\approx6.85$. Divisors of 47: 1 and 47 (since 2, 3, 4, 5, 6 do not divide 47). So, 47 is prime.
• For 79: It is greater than 1. $\sqrt{79}\approx8.89$. Divisors of 79: 1 and 79 (2 - 8 do not divide 79). So, 79 is prime.
• For 38: $38 = 2\times19$. It has divisors other than 1 and 38 (2 and 19). So, 38 is composite.
• For 22: $22 = 2\times11$. It has divisors other than 1 and 22 (2 and 11). So, 22 is composite.
• For 65: $65 = 5\times13$. It has divisors other than 1 and 65 (5 and 13). So, 65 is composite.

Answer:

Prime Numbers: 2, 47, 79
Composite Numbers: 38, 22, 65