Examine the following numbers for divisibility by 7:
28546

Answer

To determine if the number 28546 is divisible by 7, we can follow the steps outlined in the video transcript. Here’s a step-by-step solution:

### Step 1: Remove the last digit
- The last digit of 28546 is 6.
- Removing the last digit gives us the new number: **2854**.

### Step 2: Double the last digit and subtract
- We double the last digit (which we removed):
- \( 6 \times 2 = 12 \).
- Now, we subtract this from the new number obtained in Step 1:
- \( 2854 - 12 = 2842 \).

### Step 3: Check the result
- The result is 2842, which is still a four-digit number. We need to repeat the process.

### Step 4: Repeat Step 1
- Remove the last digit of 2842:
- The last digit is 2.
- Removing it gives us: **284**.

### Step 5: Double the last digit and subtract
- Double the last digit (which we removed):
- \( 2 \times 2 = 4 \).
- Now, subtract this from the new number obtained in Step 4:
- \( 284 - 4 = 280 \).

### Step 6: Check the result
- The result is 280, which is still a three-digit number. We need to repeat the process again.

### Step 7: Repeat Step 1
- Remove the last digit of 280:
- The last digit is 0.
- Removing it gives us: **28**.

### Step 8: Double the last digit and subtract
- Double the last digit (which we removed):
- \( 0 \times 2 = 0 \).
- Now, subtract this from the new number obtained in Step 7:
- \( 28 - 0 = 28 \).

### Step 9: Check the result
- The result is 28, which is a two-digit number. Now we check if 28 is divisible by 7:
- \( 28 \div 7 = 4 \) (which is a whole number).

### Conclusion
Since 28 is divisible by 7, we conclude that **28546 is also divisible by 7**.

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