Determine whether a number is prime

Detailed Explanation: Determine whether a number is prime

A prime number is a whole number greater than $1$ with exactly two factors: $1$ and the number itself.

To decide whether a number is prime:

1. Check whether it is $1$. The number $1$ is not prime.
2. Check for factor pairs besides $1$ and the number.
3. If no other factor pairs exist, the number is prime.
4. Remember that $2$ is the only even prime number. Any other even number has $2$ as a factor.

Example: Is $29$ prime?

• Start with the factor pair $1 \times 29$.
• Check whether $2$, $3$, $4$, or $5$ divides $29$:
  • $29$ is not even, so $2$ is not a factor.
  • The digits add to $2+9=11$, so $3$ is not a factor.
  • Since $4$ is even, it cannot be a factor of the odd number $29$.
  • $29$ does not end in $0$ or $5$, so $5$ is not a factor.
• Any other factor would need to pair with one of these smaller numbers. Since $6 \times 6=36$, which is greater than $29$, there are no other possible factor pairs to check.

The only factor pair is $1 \times 29$, so $29$ is prime.