If a number is divisible by 12, it means that it can be divided evenly by 12, which results in a whole number without any remainder.
The number 12 can be factored into its prime factors as follows:
- 12 = 2 × 2 × 3 = 22 × 3
Given this prime factorization, any number that is divisible by 12 will also be divisible by any combination of its prime factors and their products. Therefore, the other numbers that a number divisible by 12 will also be divisible by include:
- 1 (since every integer is divisible by 1)
- 2 (as 12 is even)
- 3 (since 12 can be divided by 3 with a whole number result)
- 4 (as 12 divided by 4 equals 3)
- 6 (since 12 divided by 6 equals 2)
- 12 itself
Additionally, any multiple of these divisors will also be included. For instance, if you take any number that is a multiple of 12, such as 24, 36, or 48, it will continue to share these same divisors, as they all include 12 as a factor.
In summary, if a number is divisible by 12, it will also be divisible by:
- 1
- 2
- 3
- 4
- 6
- 12
This understanding can be particularly useful in various mathematical contexts, including simplifying fractions and solving problems related to divisibility.