Examine the following numbers for divisibility by 6:
901352

Answer

To determine if the number 901352 is divisible by 6, we need to check if it meets the criteria for divisibility by both 2 and 3.

### Step-by-Step Solution:

**Step 1: Check for divisibility by 2.**
- A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
- The last digit of 901352 is 2, which is even.

**Conclusion for Step 1:**
- Since the last digit is 2, **901352 is divisible by 2.**

**Step 2: Check for divisibility by 3.**
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- Let's add the digits of 901352:
- 9 + 0 + 1 + 3 + 5 + 2 = 20

**Step 3: Check if the sum (20) is divisible by 3.**
- Now, we need to see if 20 is divisible by 3.
- When we divide 20 by 3, we get:
- 20 ÷ 3 = 6 remainder 2
- Since there is a remainder, 20 is not divisible by 3.

**Conclusion for Step 2:**
- Since the sum of the digits (20) is not divisible by 3, **901352 is not divisible by 3.**

**Final Conclusion:**
- Since 901352 is divisible by 2 but not by 3, it is **not divisible by 6**.

### Summary:
- 901352 is divisible by 2.
- 901352 is not divisible by 3.
- Therefore, 901352 is not divisible by 6.

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