015. Prime Factorisation Using Factor Trees

Learning Intentions

• To understand that composite numbers can be broken down into a product of prime factors
• Use a factor tree to Solve the prime factors of a number (including repeated factors)
• express a prime decomposition Use powers of prime numbers

Pre-requisite Summary

• Understanding prime and composite numbers
• Ability to find factors of a number
• Knowledge of multiplication facts
• Understanding repeated factors
• Familiarity with powers (index notation)

Worked Examples

Worked Example 1

Break into prime factors:

a)

b)

Worked Example 2

Use a factor tree:

a)

b)

Worked Example 3

Use a factor tree with repeated factors:

a)

b)

Worked Example 4

Write prime factorisation using powers:

a)

b)

Problems

Problem 1

Break into prime factors:

a)

b)

Problem 2

Use a factor tree:

a)

b)

Problem 3

Use a factor tree with repeated factors:

a)

b)

Problem 4

Write prime factorisation using powers:

a)

b)

Exercises

Understanding and Fluency

Exercise 1.

Find prime factors:

a)

b)

c)

Exercise 2.

Use factor trees:

a)

b)

c)

Exercise 3.

Find prime factors (with repeats):

a)

b)

c)

Exercise 4.

Write using powers of primes:

a)

b)

c)

Exercise 5.

Write using powers of primes:

a)

b)

c)

Exercise 6.

Mixed practice:

a)

b)

c)

Reasoning

Exercise 7.

Explain why prime factorisation of a number is unique.

Exercise 8.

A student stops factorising . Explain why this is incomplete.

Exercise 9.

Why must factor trees end only in prime numbers?

Exercise 10.

Explain why and share some prime factors.

Problem-solving

Exercise 11.

Find two different numbers with prime factorisation .

Exercise 12.

A number has prime factors . What is the number?

Exercise 13.

Find the prime factorisation of and write using powers.

Exercise 14.

Which number has prime factorisation ?

Exercise 15.

Find two numbers less than that share the same prime factors.

Potential Misunderstandings

• Students may stop factor trees before reaching prime numbers
• Students may include composite numbers in final factorisation
• Students may forget repeated prime factors
• Students may incorrectly convert repeated factors into powers
• Students may think different factor trees give different prime factorisations
• Students may confuse factors with prime factors

Next: 016. Squares, Roots and Perfect Squares