NumberKey Stage 3

Writing prime factorisation in index form

Collect repeated prime factors using powers.

  • Start with a complete prime factorisation.
  • Count how many times each prime appears.
  • Use that count as its index, then write the primes in increasing order.

Example 1

Write as a product of prime factors in index form.

Prime factor tree for 72. 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 in index form.

Prime factor tree for 180. Circled leaves are prime.

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

Remember
Use that count as its index, then write the primes in increasing order.

Your turn

Question 1

Write as a product of prime factors in index form.

Check answerPrime factor tree for 68. 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 in index form.

Check answerPrime factor tree for 21. 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 in index form.

Check answerPrime factor tree for 185. 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 in index form.

Check answerPrime factor tree for 14. 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 in index form.

Check answerPrime factor tree for 213. Circled leaves are prime.

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

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