Is 12 Prime or Composite?
Is 12 prime or composite number? Day to day, the number 12 is a composite number because it has more than two positive divisors and can be written as the product of two smaller positive integers. Its positive divisors are 1, 2, 3, 4, 6, and 12, so 12 is not prime It's one of those things that adds up..
What Is a Prime Number?
A prime number is a whole number greater than 1 that has exactly two positive divisors: 1 and the number itself. Simply put, a prime number can be divided evenly only by those two numbers.
For example:
- 2 is prime because its only divisors are 1 and 2.
- 3 is prime because its only divisors are 1 and 3.
- 5 is prime because its only divisors are 1 and 5.
- 7 is prime because its only divisors are 1 and 7.
The number 2 is the smallest prime number. In real terms, it is also the only even prime number. Every other even number greater than 2 can be divided by 2, giving it at least one additional divisor.
A simple way to test whether a number is prime is to list its positive divisors. If the list contains more than two numbers, the number is not prime.
What Is a Composite Number?
A composite number is a whole number greater than 1 that has more than two positive divisors. Composite numbers can also be expressed as a product of two smaller positive integers The details matter here. Turns out it matters..
Examples include:
- 4 = 2 × 2
- 6 = 2 × 3
- 8 = 2 × 4
- 9 = 3 × 3
- 10 = 2 × 5
- 12 = 3 × 4
Since 12 can be written as 3 × 4, it immediately meets the definition of a composite number. It is also divisible by 2, 3, 4, and 6, in addition to 1 and 12.
It is important to remember that 1 is neither prime nor composite. It has only one positive divisor, so it does not have the two divisors required for a prime number. It also cannot be expressed as a product of two smaller positive integers greater than 1, so it is not composite.
This is the bit that actually matters in practice.
How to Determine Whether 12 Is Prime or Composite
To determine whether 12 is prime or composite, follow these steps.
1. List the Positive Divisors
A divisor is a number that divides another number exactly, without a remainder. The positive divisors of 12 are:
- 1
- 2
- 3
- 4
- 6
- 12
You can verify each one by
