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b What is the correct way to express 60 in prime factor form?

12 Write 15 different (i.e. distinct) factor trees for the number 72

ENRICHMENT: Four distinct prime factors

13–15

13 There are 16 composite numbers that are smaller than 1000 which have four distinct (i.e. different) prime factors. For example: 546 = 2 × 3 × 7 × 13 By considering the prime factor possibilities, find all 16 composite numbers and express each of them in prime factor form.

14 A conjecture is a statement that may appear to be true but has not been proved conclusively. Goldbach’s conjecture states that ‘Every even number greater than 2 is the sum of two prime numbers.’ For example, 53 = 47 + 5.

Challenge: Try this for every even number from 4 to 50.

15 Use the internet to find the largest known prime number.