Pregunta
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21. Higher Order Thinking Larry says all numbers that have a 2 in the ones place are composite numbers. Explain if Larry i correct or incorrect.

Ask by Cox Hilton. in the United States
Jan 24,2025

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Larry is incorrect because the number **2**, which ends with a **2**, is a prime number, not a composite number.

Solución

Larry's statement is **incorrect**. While it's true that many numbers ending with a **2** in the ones place are composite, the number **2** itself is an exception. Here's a breakdown to clarify: 1. **Understanding Composite Numbers**: - A **composite number** is a positive integer that has at least one positive divisor other than **1** and itself. - In other words, composite numbers can be divided evenly by numbers other than **1** and themselves. 2. **Analyzing Numbers Ending with 2**: - Common examples include **2**, **12**, **22**, **32**, **42**, **52**, **62**, **72**, **82**, **92**, etc. 3. **Examining Specific Cases**: - **2**: - **2** is the smallest and only even **prime** number. - It can only be divided evenly by **1** and **2**. - Since it doesn't have any other divisors, **2** is **not** a composite number. - **12, 22, 32, ... 92**: - These numbers are all even and greater than **2**. - They can be divided evenly by **2** and other numbers, making them **composite**. 4. **Conclusion**: - While most numbers ending with a **2** are indeed composite, **2** itself is **prime**. - Therefore, Larry's blanket statement that *"all numbers that have a 2 in the ones place are composite numbers"* is **incorrect** because it doesn't account for the prime number **2**. **Summary**: Larry is incorrect because the number **2**, which ends with a **2**, is a prime number, not a composite number.

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Extra Insights

Larry is incorrect! While many composite numbers do have a 2 in the ones place, not all numbers with a 2 in that position are composite. For example, the number 2 itself is a prime number, not composite, since it has only two distinct positive divisors: 1 and 2. So, Larry's statement overlooks this crucial detail! To clarify, composite numbers have more than two divisors. Examples of composite numbers with a 2 in the ones place include 12, 22, and 32. However, since prime numbers like 2 exist, it's important to remember that not every number with a 2 in the ones place can fit Larry's definition!

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