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1 Find the complete set of factors for each of these numbers.

a 16 b 70 a 7 b 20 a 15 and 10 b 36, 54 and 72 a 8 and 12 b 3, 5 and 9 a 34 481 ÷ 4

2 Write down the first four multiples for each of these numbers.

3 Find the HCF of the following groups of numbers.

4 Find the LCM of the following groups of numbers.

5 Use divisibility rules to determine whether the following calculations are possible without leaving a remainder. Give a reason for each answer.

40 827 ÷ 3

824 730 ÷ 6

5 247 621 ÷ 9 a 60

6 The game of ‘clusters’ involves a group getting into smaller-sized groups as quickly as possible once a particular group size has been called out. If a year level consists of 120 students, which group sizes (of more than one person) would ensure no students are left out of a group?

7 State whether each of the following is a prime (P) or composite (C) number or neither (N). Give reasons.

1 c 13 d 0 a 35 b 36 a 5 × 5 × 5 × 5 a 34 b 14 × 32 c 51 × 104 d (12 8)2 e 92 33 × 2 b 7 × 3 × 7 × 7 × 3 × 7 × 7

8 Find the prime numbers that are factors of these numbers.

9 Simplify the following expressions by writing them as powers.

10 Expand and evaluate the following terms.

11 Express the following numbers in prime factor form, writing factors in ascending order.

24 b 180