Identify prime numbers

A prime number is a whole number greater than 1 with exactly two positive factors: 1 and the number itself; a composite number has additional factors, while 1 is neither prime nor composite. Identifying primes involves using factor pairs, divisibility rules, or organized lists such as a sieve, supporting later work with prime factorization, greatest common factors, least common multiples, and fraction operations; advanced primality testing for very large numbers is not included.

Detailed Explanation: Identify prime numbers

A prime number is a whole number greater than $1$ that has exactly two positive factors: $1$ and itself.

A number is composite if it has more factors than just $1$ and itself. The number $1$ is neither prime nor composite.

Example: Is $29$ prime?

Check that $29$ is greater than $1$ .
Test whether $29$ $29$ is divisible by small prime numbers:
- It is not divisible by $2$ because it is odd.
- It is not divisible by $3$ because $2+9=11$ , and $11$ is not divisible by $3$ .
- It is not divisible by $5$ because it does not end in $0$ or $5$ .
Any factor pair of $29$ would need to include a number no greater than $5$ , because $6 \times 6=36$ , which is greater than $29$ .
Since $29$ is not divisible by $2$ , $3$ , or $5$ , its only factor pair is

1 \times 29.

Therefore, $29$ has exactly two positive factors, $1$ and $29$ , so $29$ is prime.

Learn by doing: Identify prime numbers

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Which Number of a Pair is Prime

Earned ?