Playing with Numbers

1. True / False (1 pts)

The number 10 is a multiple of 5.

✓ Answer

True

2. True / False (1 pts)

Every multiple of 2 is an even number.

✓ Answer

True

3. True / False (1 pts)

The HCF of co-prime numbers 9 and 14 is 3.

✓ Answer

False

4. True / False (1 pts)

Multiplying any number by 1 gives the same number.

✓ Answer

True

5. True / False (1 pts)

The sum of two odd numbers is always odd.

✓ Answer

False

6. True / False (1 pts)

The number 1 is considered a prime number.

✓ Answer

False

7. True / False (1 pts)

The smallest prime number is 2.

✓ Answer

True

8. True / False (1 pts)

Zero is neither positive nor negative.

✓ Answer

True

9. True / False (1 pts)

Multiplying two negative numbers gives a positive product.

✓ Answer

True

10. True / False (1 pts)

A prime number has exactly two distinct factors: 1 and the number itself.

✓ Answer

True

11. Multiple Choice (2 pts)

What is the first step in solving 14 + 8 × 4 + 194 ÷ 7?

✓ Answer

C. Division

12. Multiple Choice (2 pts)

Which operation should be performed first according to BODMAS?

✓ Answer

D. Brackets

13. Multiple Choice (2 pts)

What is the smallest prime number?

✓ Answer

B. 2

14. Multiple Choice (2 pts)

The HCF of 4 and 15 is:

✓ Answer

A. 1

15. Multiple Choice (2 pts)

Which of the following numbers is divisible by 3?

✓ Answer

C. 54

16. Multiple Choice (2 pts)

Which number is a perfect number?

✓ Answer

A. 496

17. Multiple Choice (2 pts)

The 8th prime number minus the 12th prime number equals:

✓ Answer

B. 14

18. Multiple Choice (2 pts)

If a number is divisible by 90, it must be divisible by:

✓ Answer

C. 8 and 18

19. Multiple Choice (2 pts)

Which digit should replace '#' in 90##53 to make it divisible by 11?

✓ Answer

D. 2

20. Multiple Choice (2 pts)

What is the least number that can replace '*' in 764*52 so it is divisible by 11?

✓ Answer

A. 3

21. Fill in the Blank (2 pts)

The smallest prime number is _____.

✓ Answer

2

22. Fill in the Blank (2 pts)

A number divisible by 10 ends with _____.

✓ Answer

0

23. Fill in the Blank (2 pts)

To solve 36 ÷ 3 × 4, you should first perform the _____ operation.

✓ Answer

division

24. Fill in the Blank (2 pts)

The LCM of 3 and 4 is _____.

✓ Answer

12

25. Fill in the Blank (2 pts)

The HCF of two prime numbers always equals _____.

✓ Answer

1

26. Fill in the Blank (2 pts)

According to BODMAS, _____ should be solved first in the expression 4 + (5 × 3).

✓ Answer

brackets

27. Fill in the Blank (2 pts)

The sum of digits rule is used to check divisibility by _____.

✓ Answer

3

28. Fill in the Blank (2 pts)

The number _____ is both a factor of itself and 0.

✓ Answer

1

29. Fill in the Blank (2 pts)

Prime factorisation can be done using either the division method or the _____ method.

✓ Answer

factor tree

30. Fill in the Blank (2 pts)

A number divisible by both 5 and 9 is also divisible by _____.

✓ Answer

45

31. Word Problem (5 pts)

If a number is divisible by both 6 and 8, what is the smallest such positive number? Show your working.

✎ Worked Solution

Step 1: Find LCM of 6 and 8

Step 2: Prime factors of 6: 2, 3; Prime factors of 8: 2, 2, 2

Step 3: LCM = 2×2×2×3 = 24

Answer: 24

32. Word Problem (5 pts)

A car travels 150 km in 3 hours. What is its average speed? Show your working.

✎ Worked Solution

Step 1: Speed = Distance / Time

Step 2: Speed = 150 / 3

Answer: 50 km/h

33. Word Problem (5 pts)

Find the least number of 5-digit divisible by 45. Show your working.

✎ Worked Solution

Step 1: 5-digit number: 10000

Step 2: Prime factors of 45: 3×3×5

Step 3: Least 5-digit = 45 × 223

Answer: 10035

34. Word Problem (5 pts)

A bus stops every 8th block and a tram stops at every 12th block. What is the first block they both stop at? Show your working.

✎ Worked Solution

Step 1: Find LCM of 8 and 12

Step 2: Prime factors of 8: 2×2×2; Prime factors of 12: 2×2×3

Step 3: LCM = 2×2×2×3 = 24

Answer: 24

35. Word Problem (5 pts)

If three water tanks hold 5000L, 7500L, and 10000L respectively, what is the maximum container size to drain them exactly?

✎ Worked Solution

Step 1: Find HCF of 5000, 7500, 10000

Step 2: Prime factors of 5000: 2×2×2×5×5×5; Prime factors of 7500: 2×3×5×5×5; Prime factors of 10000: 2×2×2×5×5×5

Step 3: HCF = 5×5×5

Answer: 125

36. Word Problem (5 pts)

In a colony, there are 3 types of events every 4 days, 6 days, and 9 days. What is the first day they all coincide? Show your working.

✎ Worked Solution

Step 1: Find LCM of 4, 6, 9

Step 2: Prime factors of 4: 2×2; Prime factors of 6: 2×3; Prime factors of 9: 3×3

Step 3: LCM = 2×2×3×3 = 36

Answer: 36

37. Word Problem (5 pts)

Calculate the number that should be added to 9813 to make it divisible by 5, 8, and 10.

✎ Worked Solution

Step 1: Find LCM of 5, 8, 10

Step 2: Prime factors of 5: 5; Prime factors of 8: 2×2×2; Prime factors of 10: 2×5

Step 3: LCM = 2×2×2×5 = 40

Step 4: Sum = 9813 + x

Step 5: Solve: 9813 + x = multiple of 40

Answer: 27

38. Word Problem (5 pts)

If 764*52 needs to be divisible by 11, what single digit number replaces *? Show your working.

✎ Worked Solution

Step 1: Apply divisibility rule of 11: Sum of odd places - sum of even places

Step 2: (7+4+5)-(6+*+2)

Step 3: Solve => 16-(*+8)=0 or multiple of 11

Answer: 3

39. Word Problem (5 pts)

Determine the smallest digit added to 31290876 to make it divisible by 5, 8, and 10. Show your working.

✎ Worked Solution

Step 1: Find LCM of 5, 8, and 10

Step 2: LCM = 40

Step 3: Add digit x so that 31290876 + x

Step 4: Find smallest x such that 31290876 + x = multiple of 40

Answer: 4

40. Word Problem (5 pts)

What number should be subtracted from 1002 to make it divisible by 3 and 4? Show your working.

✎ Worked Solution

Step 1: Find LCM of 3 and 4

Step 2: Prime factors of 3: 3; Prime factors of 4: 2×2

Step 3: LCM = 2×2×3 = 12

Step 4: Solve 1002 - x = multiple of 12

Answer: 2