Is 4,578 divisible by 6?

Answer

To determine if the number 4,578 is divisible by 6, we need to check its divisibility by both 2 and 3, as a number is divisible by 6 if and only if it is divisible by both of these numbers.

### Step-by-step Solution:

**Step 1: Check divisibility by 2.**
- A number is divisible by 2 if its last digit (ones place) is one of the following: 0, 2, 4, 6, or 8.
- The last digit of 4,578 is 8.

**Conclusion for Step 1:**
Since 8 is in the list (0, 2, 4, 6, 8), 4,578 is divisible by 2.

**Step 2: Check divisibility by 3.**
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- The digits of 4,578 are 4, 5, 7, and 8.
- Calculate the sum:
\[ 4 + 5 + 7 + 8 = 24 \]

**Conclusion for Step 2:**
Now, we check if 24 is divisible by 3. Since \( 24 \div 3 = 8 \) (which is an integer), 24 is divisible by 3.

**Step 3: Combine the results.**
- Since 4,578 is divisible by both 2 and 3, we conclude that it is also divisible by 6.

### Final Answer:
Yes, 4,578 is divisible by 6.

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