HCF: Prime Factorisation

• What is prime factorisation?

  Breaking down a number into its prime numbers
• What are prime numbers?

  Numbers divisible only by 1 and themselves
• What is the process of prime factorisation for the number 12?

  1. Divide 12 by 2: $12 ÷ 2 =$$6$
  2. Divide 6 by 2: $6 ÷ 2 =$$3$
  3. Divide 3 by 3: $3 ÷ 3 =$$1$

  • Prime factors of 12: $2, 2, 3$
  • Written as: $12 =$$2^{2} × 3$
• Why is understanding prime factorisation important?

  It helps in finding the HCF later
• What is the first step to find the HCF using prime factorisation?

  Finding the prime factors of each number
• How do you break down the number 16 into prime factors?

  • $16 =$$2 × 2 × 2 × 2 =$$2^{4}$
• How do you break down the number 24 into prime factors?

  • $24 =$$2 × 2 × 2 × 3 =$$2^{3} × 3$
• What is the prime factorisation of 16?

  $2^{4}$
• What is the prime factorisation of 24?

  $2^{3} × 3$
• What do you do after breaking down each number into prime factors?

  Identify the prime factors they share in common
• What is the common prime factor of 16 and 24?


  2
• How do you determine the lowest power of each common prime factor?

  • Compare the powers of common prime factors
  • Example:
  • 16 has $2^{4}$
  • 24 has $2^{3}$
  • Lowest power is $2^{3}$
• What is the lowest power of the common prime factor 2 between 16 and 24?

  $2^{3}$
• What is the process to find the highest common factor (HCF)?

  1. Identify common prime factors
  2. Determine their lowest powers
  3. Multiply the lowest powers together
• What is the HCF of 16 and 24?

  8
• What is the final step to find the HCF using the lowest powers of common prime factors?

  • Multiply the lowest powers together
  • Example: $2^{3} =$$2 × 2 × 2 =$$8$
• What is the product of the lowest power $2^{3}$?


  8
• What is the HCF of 16 and 24?

  8