Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Which of these is not a factor of 12?
Show worked solution
12 ÷ 5 leaves a remainder, so 5 is not a factor. 1, 2, 3, 4, 6, 12 are.
2 Complete the factor pairs of 20.
Show worked solution
1 × 20, 2 × 10, 4 × 5. Factors of 20: 1, 2, 4, 5, 10, 20.
3 What is the 7th multiple of 8?
Show worked solution
8, 16, 24, 32, 40, 48, 56.
Level 2 · Core
4 What is the lowest common multiple of 4 and 6?
Show worked solution
6, then 12 — and 4 divides 12. 24 is a common multiple but not the lowest; 2 is a common factor.
5 For 12 and 18, give the highest common factor and the lowest common multiple.
Show worked solution
Shared factors 1, 2, 3, 6 → HCF 6. Multiples of 18: 18, 36 — 12 divides 36 → LCM 36.
6 How many multiples of 6 are there from 1 to 100?
Show worked solution
100 ÷ 6 = 16 remainder 4, so 16 multiples (6 up to 96).
Level 3 · Challenge
7 Buses leave a station every 12 minutes and trains every 18 minutes. A bus and a train leave together at 8:00.1 The next time they leave together is 8:36.
2 After 8:00, they leave together 3 more times before 10:00.
3 A bus and a train leave together at 9:00.
Which statements are correct?
2 After 8:00, they leave together 3 more times before 10:00.
3 A bus and a train leave together at 9:00.
Which statements are correct?
Show worked solution
LCM of 12 and 18 is 36, so together at 8:36 (1 ✓), 9:12, 9:48 — three more times before 10:00 (2 ✓). 9:00 is 60 minutes after 8:00, and 60 is not a multiple of 36 (3 ✗). 1 and 2.
8 From 1 to 100: how many multiples of 4 are there, how many are multiples of both 4 and 6, and how many are multiples of 4 but not 6?
Show worked solution
100 ÷ 4 = 25. Multiples of 12 up to 100: 12 … 96, that is 8. 25 − 8 = 17.
9 Ali's number is a multiple of 6 and less than 50. Bea's number is an odd multiple of 9. What is the difference between the largest Ali's number could be and the smallest Bea's number could be?
Show worked solution
Multiples of 6 below 50 stop at 48. Odd multiples of 9 start at 9. 48 − 9 = 39.