John was asked to give numbers between 2 and 9 that can exactly divide 234. What are these numbers?

To determine which numbers between 2 and 9 can exactly divide 234, we will find the divisors of 234 within that range. A number divides 234 exactly if the remainder when dividing is 0, i.e., 234 ÷ divisor must be an integer.

Let's check each number between 2 and 9:

1. **234 ÷ 2 = 117** (exact, so 2 is a divisor)
2. **234 ÷ 3 = 78** (exact, so 3 is a divisor)
3. **234 ÷ 4 = 58.5** (not exact, so 4 is not a divisor)
4. **234 ÷ 5 = 46.8** (not exact, so 5 is not a divisor)
5. **234 ÷ 6 = 39** (exact, so 6 is a divisor)
6. **234 ÷ 7 = 33.43** (not exact, so 7 is not a divisor)
7. **234 ÷ 8 = 29.25** (not exact, so 8 is not a divisor)
8. **234 ÷ 9 = 26** (exact, so 9 is a divisor)

### Conclusion:
The numbers between 2 and 9 that can exactly divide 234 are: **2, 3, 6, and 9**.

Would you like details on any of the steps or further explanation?

Here are five questions based on this topic:

1. What are all the divisors of 234, not limited to the range between 2 and 9?
2. How would you find the greatest common divisor (GCD) of two numbers like 234 and another number?
3. How can you determine if a number is divisible by a certain divisor without performing the division?
4. What is the prime factorization of 234?
5. How can divisibility rules be applied to quickly check divisibility by numbers like 3 or 9?

**Tip:** When checking divisibility by 3 or 9, add the digits of the number. If the sum is divisible by 3 or 9, then the number is also divisible by that divisor.

Explore how to find which numbers between 2 and 9 divide 234 exactly. This problem demonstrates key concepts in divisibility and number theory. Ideal for students in Grades 5-7, it includes divisibility rules and step-by-step calculations.

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