1. Which number is the only even prime number? 2. Write down the numbers 1 to 16 in your workbook. From that list write down the numbers that are: \( \begin{array}{llll}\text { a) neither composite nor prime } & \text { b) factors of } 27 \\ \text { c) multiples of } 4 & \text { d) prime numbers } \\ \text { e) composite numbers. } & \text { d) } \\ \begin{array}{llll}\text { 3. Which of these numbers are prime and which are composite? } \\ \text { (a) } 64 & \text { b) } 78 & \text { c) } 111 & \text { d) } 54\end{array} & \begin{array}{l}\text { numbe } \\ \text { crossec } \\ \text { multipl } \\ \text { the mul } \\ \text { then th } \\ \text { 4, and s } \\ \text { only pri } \\ \text { were lef } \\ \text { method } \\ \text { to ident } \\ \text { number } \\ \text { than } 100\end{array} \\ \begin{array}{llll}\text { f) } 37 & \text { g) } 121 & \text { h) } 172 & \text { i) } 441\end{array} & \text { j) } 324\end{array} \) 4irror primes have digits in the reverse order, like 17

Let's break down the problem step by step. ### 1. Which number is the only even prime number? The only even prime number is **2**. All other even numbers can be divided by 2, making them composite. ### 2. Write down the numbers 1 to 16 in your workbook. The numbers from 1 to 16 are: \[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 \] Now, let's categorize these numbers based on the given criteria: #### a) Neither composite nor prime The only number that is neither composite nor prime is **1**. #### b) Factors of 27 The factors of 27 are **1, 3, 9, 27**. From the list of numbers 1 to 16, the factors are: \[ 1, 3, 9 \] #### c) Multiples of 4 The multiples of 4 from 1 to 16 are: \[ 4, 8, 12, 16 \] #### d) Prime numbers The prime numbers from 1 to 16 are: \[ 2, 3, 5, 7, 11, 13 \] #### e) Composite numbers The composite numbers from 1 to 16 are: \[ 4, 6, 8, 9, 10, 12, 14, 15, 16 \] ### 3. Which of these numbers are prime and which are composite? Let's analyze the numbers given: - **(a) 64**: Composite (it can be divided by 2, 4, 8, etc.) - **(b) 78**: Composite (it can be divided by 2, 3, 6, etc.) - **(c) 111**: Composite (it can be divided by 3, 37) - **(d) 54**: Composite (it can be divided by 2, 3, 6, etc.) Now for the additional numbers: - **(f) 37**: Prime - **(g) 121**: Composite (it is \(11^2\)) - **(h) 172**: Composite (it can be divided by 2) - **(i) 441**: Composite (it is \(21^2\)) - **(j) 324**: Composite (it is \(18^2\)) ### 4. Mirror primes Mirror primes are pairs of prime numbers that have digits in reverse order. For example, 17 and 71 are mirror primes. From the prime numbers identified earlier (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997) we can identify pairs like (13, 31), (17, 71), (37, 73), etc. This concludes the analysis of the problem. If you have any further questions or need additional assistance, feel free to ask!