What are Numbers Divisible by 12?
A number is divisible by 12 if it's divisible by both 3 and 4. This is because 12's prime factorization is 2 x 2 x 3 (or 2² x 3). Therefore, any number containing these prime factors will be divisible by 12.
To determine if a number is divisible by 12, follow these steps:
- Divisibility by 3: Check if the sum of the digits is divisible by 3.
- Divisibility by 4: Check if the last two digits are divisible by 4.
If both conditions are true, the number is divisible by 12.
Examples
- 144: Sum of digits (1+4+4=9) is divisible by 3. The last two digits (44) are divisible by 4. Therefore, 144 is divisible by 12.
- 360: Sum of digits (3+6+0=9) is divisible by 3. The last two digits (60) are divisible by 4. Therefore, 360 is divisible by 12.
- 252: Sum of digits (2+5+2=9) is divisible by 3. The last two digits (52) are divisible by 4. Therefore, 252 is divisible by 12.
- 108: The sum of the digits (1+0+8=9) is divisible by 3. The last two digits (08 or 8) is not divisible by 4. Therefore 108 is not divisible by 12.
- 636: Sum of digits (6+3+6=15) is divisible by 3, and the last two digits (36) are divisible by 4. Therefore, 636 is divisible by 12.
Multiples of 12
The multiples of 12 are numbers that result from multiplying 12 by any whole number. Examples include: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so on. NumberGenerator.org provides a more extensive list.
Other Divisibility Considerations
A number divisible by 12 is also divisible by its factors: 1, 2, 3, 4, 6, and 12. This is a direct consequence of the prime factorization. As noted in several sources (Smartick, Cuemath, Reddit), understanding the prime factors helps in identifying all possible divisors.
