Skill: Determine whether a number is prime

Explanation and Free Practice Resources

A prime number is a whole number greater than 1 with exactly two distinct factors, 1 and itself; 2 is the only even prime, while 1 is neither prime nor composite. Determining whether a number is prime involves examining its factor pairs or divisibility by possible factors, with the focus on whole numbers through 100 rather than very large numbers or advanced primality-testing methods; this understanding supports prime factorization and work with common factors and multiples.

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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:

Check whether it is $1$ . The number $1$ is not prime.
Check for factor pairs besides $1$ and the number.
If no other factor pairs exist, the number is prime.
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 $2$ $2$ , $3$ $3$ , $4$ $4$ , or $5$ $5$ divides $29$ $29$ :
- $29$ 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.

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