Prime Factorisation

• What is a prime number?

  A number greater than 1 with two factors
• How many factors does a prime number have?

  Exactly two factors
• What is a composite number?

  A number with more than two factors
• How can composite numbers be divided?

  By 1, themselves, and at least one other number
• What is the prime factorisation process?

  1. Start with a composite number
  2. Divide by the smallest prime number
  3. Repeat division with the quotient
  4. Stop when the quotient is prime
  5. Express as a product of prime factors
• What is the first step in the prime factorisation process?

  Start with a composite number
• What is the result of $12 \div 2$?


  $6$
• What do you do after dividing $6 \div 2$?


  Repeat the division with the quotient
• What is the prime factorisation of 12?

  $12 =$$2^{2} \times 3$
• What are the steps to find prime factors using division?

  1. Start with the number
  2. Divide by the smallest prime number
  3. Repeat division with the new quotient
  4. Continue dividing by primes
  5. Collect all prime factors
• What is the first step to find the prime factors of 36?

  Start with the number 36
• What is the result of $36 \div 2$?


  $18$
• What do you do after $18 \div 2$?


  Divide by 3
• What are the prime factors of 36?

  2, 2, 3, 3
• How do you express a number as a product of prime factors?

  • Break down into prime components
  • Multiply them together
• What is the prime factorisation of 24?

  $24 =$$2^{3} \times 3$
• What is the prime factorisation of 60?

  $60 =$$2^{2} \times 3 \times 5$
• What are the steps to prime factorise 28?

  1. Divide by 2: $28 \div 2 =$$14$
  2. Divide by 2: $14 \div 2 =$$7$
  3. Express as product: $28 =$$2^{2} \times 7$
• What are the steps to prime factorise 45?

  1. Divide by 3: $45 \div 3 =$$15$
  2. Divide by 3: $15 \div 3 =$$5$
  3. Express as product: $45 =$$3^{2} \times 5$