To determine which of the given numbers are divisible by 12, we need to apply the divisibility rules for 12. Specifically, a number is divisible by 12 if and only if it is divisible by both 3 and 4.
1. Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
2. Divisibility by 4: A number is divisible by 4 if the last two digits of the number form a number that is divisible by 4.
Let's go through each number:
1. 896436
- Sum of digits: 8 + 9 + 6 + 4 + 3 + 6 = 36 (which is divisible by 3)
- Last two digits: 36 (which is divisible by 4)
- Therefore, 896436 is divisible by 12.
2. 348232
- Sum of digits: 3 + 4 + 8 + 2 + 3 + 2 = 22 (which is not divisible by 3)
- Therefore, 348232 is not divisible by 12 without need to check divisibility by 4.
3. 273942
- Sum of digits: 2 + 7 + 3 + 9 + 4 + 2 = 27 (which is divisible by 3)
- Last two digits: 42 (which is not divisible by 4)
- Therefore, 273942 is not divisible by 12.
4. 3456780
- Sum of digits: 3 + 4 + 5 + 6 + 7 + 8 + 0 = 33 (which is divisible by 3)
- Last two digits: 80 (which is divisible by 4)
- Therefore, 3456780 is divisible by 12.
5. 2489224
- Sum of digits: 2 + 4 + 8 + 9 + 2 + 2 + 4 = 31 (which is not divisible by 3)
- Therefore, 2489224 is not divisible by 12 without need to check divisibility by 4.
6. 843384
- Sum of digits: 8 + 4 + 3 + 3 + 8 + 4 = 30 (which is divisible by 3)
- Last two digits: 84 (which is divisible by 4)
- Therefore, 843384 is divisible by 12.
So, the numbers that are divisible by 12 are 896436, 3456780, and 843384.
