NumberKey Stage 3

Prime factorisation using a factor tree

Break a whole number into prime factors.

  • Split the number into any useful pair of factors.
  • Keep splitting composite factors until every endpoint is prime.
  • Multiply all the prime endpoints to check the original number.

Example 1

Write as a product of prime factors.

Prime factor tree for 60. Circled leaves are prime.

Every circled endpoint is prime. Multiply all the endpoints to reconstruct the original number.

Example 2

Write as a product of prime factors.

Prime factor tree for 72. Circled leaves are prime.

Every circled endpoint is prime. Multiply all the endpoints to reconstruct the original number.

Remember
Multiply all the prime endpoints to check the original number.

Your turn

Question 1

Write as a product of prime factors.

Check answerPrime factor tree for 117. Circled leaves are prime.

Every circled endpoint is prime. Multiply all the endpoints to reconstruct the original number.

Question 2

Write as a product of prime factors.

Check answerPrime factor tree for 84. Circled leaves are prime.

Every circled endpoint is prime. Multiply all the endpoints to reconstruct the original number.

Question 3

Write as a product of prime factors.

Check answerPrime factor tree for 200. Circled leaves are prime.

Every circled endpoint is prime. Multiply all the endpoints to reconstruct the original number.

Question 4

Write as a product of prime factors.

Check answerPrime factor tree for 158. Circled leaves are prime.

Every circled endpoint is prime. Multiply all the endpoints to reconstruct the original number.

Question 5

Write as a product of prime factors.

Check answerPrime factor tree for 217. Circled leaves are prime.

Every circled endpoint is prime. Multiply all the endpoints to reconstruct the original number.