To determine which numbers 315 is divisible by, we can use divisibility tests for common divisors:

1. Divisibility by 2: A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8.

   • 315 ends in 5, so it is not divisible by 2.

2. Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.

   • Sum of digits of 315: $3 + 1 + 5 = 9$.
   • 9 is divisible by 3, so 315 is divisible by 3.

3. Divisibility by 5: A number is divisible by 5 if it ends in 0 or 5.

   • 315 ends in 5, so it is divisible by 5.

4. Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.

   • 315 is not divisible by 2 (as checked above), so it is not divisible by 6.

5. Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

   • The sum of digits is 9 (as calculated above).
   • 9 is divisible by 9, so 315 is divisible by 9.

Summary:

• 315 is divisible by 3, 5, and 9.
• 315 is not divisible by 2 or 6.

Would you like more details or have any questions about this? Here are some related questions:

1. How do you test divisibility by 4 and 8?
2. What is the divisibility rule for 7, and does it apply to 315?
3. Can you find the prime factorization of 315?
4. Is 315 divisible by 10, and why or why not?
5. How do divisibility rules help in simplifying fractions?

Tip: Understanding divisibility rules can greatly speed up factoring and simplifying problems in arithmetic.