Of the numbers 29540, 53416 and 21543

Options

A. none is divisible by 12
B. one is divisible by 12
C. two are divisible by 12
D. all are divisible by 12

Answer

To determine which of the numbers 29540, 53416, and 21543 are divisible by 12, we need to check their divisibility by both 4 and 3, as 12 is the product of these two numbers.

### Step-by-Step Solution:

1. **Check divisibility by 4:**
- A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- For 29540, the last two digits are 40.
- \( 40 \div 4 = 10 \) (divisible)
- For 53416, the last two digits are 16.
- \( 16 \div 4 = 4 \) (divisible)
- For 21543, the last two digits are 43.
- \( 43 \div 4 = 10.75 \) (not divisible)

**Conclusion:** 29540 and 53416 are divisible by 4, while 21543 is not.

2. **Check divisibility by 3:**
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- For 29540, the sum of the digits is \( 2 + 9 + 5 + 4 + 0 = 20 \).
- \( 20 \div 3 \) gives a remainder (not divisible)
- For 53416, the sum of the digits is \( 5 + 3 + 4 + 1 + 6 = 19 \).
- \( 19 \div 3 \) gives a remainder (not divisible)
- For 21543, the sum of the digits is \( 2 + 1 + 5 + 4 + 3 = 15 \).
- \( 15 \div 3 = 5 \) (divisible)

**Conclusion:** Only 21543 is divisible by 3, while 29540 and 53416 are not.

3. **Check divisibility by 12:**
- A number is divisible by 12 if it is divisible by both 4 and 3.
- 29540: Divisible by 4 (yes), Divisible by 3 (no) → Not divisible by 12.
- 53416: Divisible by 4 (yes), Divisible by 3 (no) → Not divisible by 12.
- 21543: Divisible by 4 (no), Divisible by 3 (yes) → Not divisible by 12.

### Final Conclusion:
None of the numbers 29540, 53416, or 21543 are divisible by 12.

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