Lesson 1: Exploring Factors, Multiples, and Number Types

Property

A prime number is a counting number greater than 1 whose only factors are 1 and itself.
A composite number is a counting number that is not prime. The number 1 is neither prime nor composite.

To determine if a number is prime:

1. Test each of the primes (2, 3, 5, ...), in order, to see if it is a factor of the number.
2. Stop when the quotient is smaller than the divisor or when a prime factor is found.
3. If it has a prime factor, it is composite. If not, it is prime.

Examples

• Is 29 a prime number? It is not divisible by 2 (it is odd), 3 (sum of digits is 11), or 5. Testing 7 gives $29 \div 7$, which has a remainder. Since the next quotient is smaller than the divisor, 29 is prime.

Property

• A factor is a whole number that divides exactly into another number. If $a \times b = c$, then $a$ and $b$ are factors of $c$.
• A multiple of a number is the result of multiplying that number by a counting number (1, 2, 3, ...).

Examples