To determine which numbers are divisible by 9, we use the rule of divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

Steps:

1. Calculate the sum of the digits of each number.
2. Check if the sum is divisible by 9.

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Checking:

1. 171

   • Sum of digits: $1 + 7 + 1 = 9$
   • $9 \div 9 = 1$ → Divisible by 9 ✅

2. 258

   • Sum of digits: $2 + 5 + 8 = 15$
   • $15 \div 9 = 1.666...$ → Not divisible by 9 ❌

3. 468

   • Sum of digits: $4 + 6 + 8 = 18$
   • $18 \div 9 = 2$ → Divisible by 9 ✅

4. 699

   • Sum of digits: $6 + 9 + 9 = 24$
   • $24 \div 9 = 2.666...$ → Not divisible by 9 ❌

5. 1251

   • Sum of digits: $1 + 2 + 5 + 1 = 9$
   • $9 \div 9 = 1$ → Divisible by 9 ✅

6. 2889

   • Sum of digits: $2 + 8 + 8 + 9 = 27$
   • $27 \div 9 = 3$ → Divisible by 9 ✅

7. 79874

   • Sum of digits: $7 + 9 + 8 + 7 + 4 = 35$
   • $35 \div 9 = 3.888...$ → Not divisible by 9 ❌

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Final Answer:

The numbers divisible by 9 are: 171, 468, 1251, and 2889

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Would you like more details on this process or further questions? Here are related prompts:

1. How do divisibility rules work for numbers other than 9?
2. Can you show a step-by-step solution for a specific number again?
3. Why does the sum of digits rule work for divisibility by 9?
4. Can you write a program to check divisibility by 9 for any given number?
5. What are common errors when applying divisibility rules?

Tip: To quickly check divisibility by 9, practice adding digits mentally in groups!