← Back to view Tip: choose "Save as PDF" as your printer for a clean PDF
Answer Key — Teacher Copy
Mathematics

Playing with Numbers Worksheet

Operations, BODMAS, Multiples, Factors and Divisibility
Date: May 31, 2026  •  40 questions  •  Total: 100 points
StudentAayush Nayak
Class6-B
GradeGrade 6
SchoolYBIS
1. True / False (1 pts)
The rabbit takes one step forward for each correct answer.
✓ Answer
True
2. True / False (1 pts)
The result of 4 × 100 + 7 × 10 + 3 is 473.
✓ Answer
True
3. True / False (1 pts)
According to the BODMAS rule, operations inside brackets are performed first.
✓ Answer
True
4. True / False (1 pts)
In a multi-operation problem, subtraction is always carried out first.
✓ Answer
False
5. True / False (1 pts)
The property LCM × HCF = Product of two numbers holds true for any pair of numbers.
✓ Answer
True
6. True / False (1 pts)
Prime factorization involves breaking down a number into its prime factors.
✓ Answer
True
7. True / False (1 pts)
A prime number has more than two distinct factors.
✓ Answer
False
8. True / False (1 pts)
Multiples of a number are obtained by repeatedly adding the number to itself.
✓ Answer
True
9. True / False (1 pts)
If a number is divisible by both 9 and 11, it is always divisible by 90.
✓ Answer
False
10. True / False (1 pts)
A perfect number is one that is equal to the sum of its proper divisors.
✓ Answer
True
11. Multiple Choice (2 pts)
What is 4 × 100 + 7 × 10 + 3?
✓ Answer
A. 473
12. Multiple Choice (2 pts)
What is 10 less than 10 times 51?
✓ Answer
A. 500
13. Multiple Choice (2 pts)
What is the simplified form of 5 × 10,000 + 9 × 10 + 1?
✓ Answer
A. 50091
14. Multiple Choice (2 pts)
According to the BODMAS rule, which operation should be performed first?
✓ Answer
C. Brackets
15. Multiple Choice (2 pts)
The HCF of two coprime numbers is:
✓ Answer
B. 1
16. Multiple Choice (2 pts)
In prime factorization, which number is considered the smallest prime?
✓ Answer
B. 2
17. Multiple Choice (2 pts)
Which of the following numbers is divisible by 3?
✓ Answer
B. 54
18. Multiple Choice (2 pts)
What does LCM stand for?
✓ Answer
A. Least Common Multiple
19. Multiple Choice (2 pts)
What is the key concept behind the factor tree method?
✓ Answer
A. Division into prime factors
20. Multiple Choice (2 pts)
Which statement is true about prime numbers?
✓ Answer
B. 2 is the only even prime number
21. Fill in the Blank (2 pts)
In the number 4 × 100 + 7 × 10 + 3, the digit in the tens place is _____ .
✓ Answer
7
22. Fill in the Blank (2 pts)
The result of 10 times 51 minus 10 is _____ .
✓ Answer
500
23. Fill in the Blank (2 pts)
The simplified expression for 5 × 10,000 + 9 × 10 + 1 is _____ .
✓ Answer
50091
24. Fill in the Blank (2 pts)
According to the BODMAS rule, operations inside _____ are performed first.
✓ Answer
brackets
25. Fill in the Blank (2 pts)
The smallest factor of every number is _____ .
✓ Answer
1
26. Fill in the Blank (2 pts)
Prime factorization breaks a number into its _____ factors.
✓ Answer
prime
27. Fill in the Blank (2 pts)
LCM stands for Least Common _____ .
✓ Answer
Multiple
28. Fill in the Blank (2 pts)
The property LCM × HCF = Product of two numbers shows the relation between _____.
✓ Answer
multiples and factors
29. Fill in the Blank (2 pts)
Divisibility by 3 is determined by the sum of the _____ of a number.
✓ Answer
digits
30. Fill in the Blank (2 pts)
A perfect number is one that is equal to the sum of its _____ divisors.
✓ Answer
proper
31. Word Problem (5 pts)
A rabbit hops forward each time a correct answer is given. If it takes 473 steps to reach a carrot, and each correct answer moves it 1 step, how many correct answers did it get? Show your working.
✎ Worked Solution
Step 1: Recognize each correct answer equals 1 step
Step 2: Total steps = 473
Answer: 473
32. Word Problem (5 pts)
Solve: 10 less than 10 times 51. Show your working.
✎ Worked Solution
Step 1: Calculate 10 × 51 = 510
Step 2: Subtract 10: 510 - 10
Answer: 500
33. Word Problem (5 pts)
Evaluate: 5 × 10,000 + 9 × 10 + 1 × 1. Show your working.
✎ Worked Solution
Step 1: Calculate 5 × 10,000 = 50000
Step 2: Calculate 9 × 10 = 90
Step 3: Add 50000 + 90 + 1
Answer: 50091
34. Word Problem (5 pts)
Calculate 36,000 + 400 - 100 + 10. Show your working.
✎ Worked Solution
Step 1: Add 36,000 + 400 = 36400
Step 2: Subtract 100: 36400 - 100 = 36300
Step 3: Add 10: 36300 + 10
Answer: 36310
35. Word Problem (5 pts)
Find the least common multiple (LCM) of 15 and 20. Show your working.
✎ Worked Solution
Step 1: Prime factors: 15 = 3 × 5, 20 = 2² × 5
Step 2: LCM = 2² × 3 × 5
Answer: 60
36. Word Problem (5 pts)
Determine the highest common factor (HCF) of 36 and 60. Show your working.
✎ Worked Solution
Step 1: Prime factors: 36 = 2² × 3², 60 = 2² × 3 × 5
Step 2: HCF = 2² × 3
Answer: 12
37. Word Problem (5 pts)
A six-digit number has digits that sum to 27. Explain why this number is divisible by 9. Show your working.
✎ Worked Solution
Step 1: Sum of digits = 27
Step 2: Since 27 ÷ 9 = 3 exactly
Answer: The number is divisible by 9
38. Word Problem (5 pts)
In a colony with 62 blocks, a bus stops every 10th block and a van every 6th block. What is the first block where both vehicles stop? Show your working.
✎ Worked Solution
Step 1: Find LCM of 6 and 10 = 30
Step 2: First common stop is block 30
Answer: 30
39. Word Problem (5 pts)
If the property LCM × HCF = Product of two numbers holds, and the LCM of two numbers is 60 while the HCF is 12, find the product of the two numbers. Show your working.
✎ Worked Solution
Step 1: Multiply LCM and HCF: 60 × 12
Step 2: Compute the product
Answer: 720
40. Word Problem (5 pts)
Three water tankers have capacities of 5000, 8000, and 10,000 litres. What is the maximum capacity of a container that can measure all three tanks exactly? Show your working.
✎ Worked Solution
Step 1: Find HCF of 5000, 8000, and 10000
Step 2: HCF = 1000
Answer: 1000