013. Prime Numbers and Prime Factorisation

Learning Intentions

• To know what prime numbers and composite numbers are
• Determine whether a number is prime by considering its factors
• Solve the prime factors of a given number

Pre-requisite Summary

• Understanding factors and multiples
• Knowledge that and the number itself are always factors
• Ability to test divisibility by small numbers ()
• Understanding multiplication as forming composite numbers
• Familiarity with division and factor pairs

Worked Examples

Worked Example 1

Identify numbers as prime or composite:

a)

b)

c)

Worked Example 2

Determine if the number is prime by considering factors:

a)

b)

c)

Worked Example 3

Find prime factors:

a)

b)

Worked Example 4

Find prime factors:

a)

b)

Problems

Problem 1

Classify as prime or composite:

a)

b)

c)

Problem 2

Determine if prime:

a)

b)

c)

Problem 3

Find prime factors:

a)

b)

Problem 4

Find prime factors:

a)

b)

Exercises

Understanding and Fluency

Exercise 1.

Classify as prime or composite:

a)

b)

c)

Exercise 2.

Classify as prime or composite:

a)

b)

c)

Exercise 3.

Determine if prime by considering factors:

a)

b)

c)

Exercise 4.

Determine if prime by considering factors:

a)

b)

c)

Exercise 5.

Find prime factors:

a)

b)

c)

Exercise 6.

Find prime factors:

a)

b)

c)

Reasoning

Exercise 7.

Explain why is not a prime number.

Exercise 8.

Why must every composite number have at least one prime factor?

Exercise 9.

A student says is prime because it is odd. Explain the mistake.

Exercise 10.

Explain why is the only even prime number.

Problem-solving

Exercise 11.

Find two different composite numbers that have the same prime factors.

Exercise 12.

Find a number whose prime factors are and .

Exercise 13.

Find all prime numbers between and .

Exercise 14.

A number has prime factorisation . What is the number?

Exercise 15.

Find a number less than with three prime factors.

Potential Misunderstandings

• Students may think is a prime number
• Students may think all odd numbers are prime
• Students may stop checking factors too early
• Students may include composite numbers when listing prime factors
• Students may forget to continue factorising until only primes remain
• Students may confuse prime factorisation with listing all factors

Next: 014. Powers and Index Notation