Class 8 Maths Chapter 5 – Number Play

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Practise Class 8 Maths Chapter 5 Number Play MCQs Set 1 based on NCERT concepts, including divisibility rules, factors, multiples, parity, and number patterns with detailed explanations.

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Chapter Information

• Class: 8
• Subject: Mathematics
• Chapter: 5 – Number Play
• Practice Set: 1
• Board: CBSE
• Textbook Reference: NCERT Ganita Prakash, Part I
• Question Type: Multiple-Choice Questions (MCQs)

Introduction

Numbers have interesting properties that help us solve mathematical problems quickly and logically. In Chapter 5, Number Play, students explore divisibility, factors, multiples, even and odd numbers, and patterns in arithmetic expressions.

This practice set introduces important concepts related to divisibility and number properties. The questions are designed to improve mathematical reasoning and help students understand why certain divisibility rules work.

What Will You Learn?

After completing this practice set, students will be able to:

• Understand the relationship between factors and multiples.
• Apply basic divisibility rules.
• Identify even and odd numbers using arithmetic expressions.
• Understand how divisibility behaves under addition.
• Recognise important properties of numbers.

Why Is This Topic Important?

Divisibility and number properties are useful for simplifying calculations, identifying factors, and solving mathematical puzzles. Understanding these concepts also helps students develop logical reasoning skills and prepare for more advanced topics in mathematics.

Exam Relevance

Questions from this chapter may test students’ understanding of:

• Divisibility rules for different numbers.
• Factors and multiples.
• Even and odd numbers.
• Addition and subtraction of multiples.
• Logical reasoning involving number properties.

MCQs with Detailed Solutions

Question 1: Understanding Even and Odd Numbers

Consider the expression:

$$3+4-5+6$$

What is the correct result, and what does it tell us about the expression?

A. 6, which is an odd number.

B. 8, which is an even number.

C. 10, which is an odd number.

D. 12, which is an even number.

Answer: B. 8, which is an even number.

Concept: Addition and subtraction involving integers.

Explanation:

Evaluate the expression from left to right:

$$3+4=7$$

$$7-5=2$$

$$2+6=8$$

The result is 8, which is an even number because it is divisible by 2.

Therefore, option B is correct.

Correct Answer: B. 8, which is an even number.

Question 2: Divisibility Under Addition

A number 24 is divisible by 8, and another number 40 is also divisible by 8. Which statement about their sum is correct?

A. Their sum is not divisible by 8.

B. Their sum is divisible by 4 but not by 8.

C. Their sum is divisible by 8.

D. Their sum is divisible by 3 but not by 8.

Answer: C. Their sum is divisible by 8.

Concept: The sum of two multiples of the same number is also a multiple of that number.

Explanation:

Both numbers are divisible by 8:

$$24=8\times3$$

$$40=8\times5$$

Adding them gives:

$$24+40=64$$

Now divide the sum by 8:

$$64\div8=8$$

Since the quotient is a whole number, 64 is divisible by 8.

In general, if two numbers are multiples of (k), their sum is also a multiple of (k).

Correct Answer: C. Their sum is divisible by 8.

Question 3: Factors and Divisibility

If a number is divisible by 12, which of the following numbers must also divide it exactly?

A. 5

B. 7

C. 9

D. 3

Answer: D. 3

Concept: Every factor of a number divides that number and all its multiples.

Explanation:

The factors of 12 include:

$$1,\ 2,\ 3,\ 4,\ 6,\ 12$$

If a number is divisible by 12, it can be expressed as:

$$N=12k$$

where (k) is an integer.

Since:

$$12=3\times4$$

we can write:

$$N=3\times(4k)$$

Therefore, (N) is always divisible by 3.

It is not necessarily divisible by 5, 7, or 9.

Correct Answer: D. 3

Question 4: Divisibility Rule for 9

Which of the following numbers is divisible by 9?

A. 725

B. 731

C. 729

D. 742

Answer: C. 729

Concept: Divisibility rule for 9.

Explanation:

A number is divisible by 9 if the sum of its digits is divisible by 9.

Check each option:

Option A: 725

$$7+2+5=14$$

14 is not divisible by 9.

Option B: 731

$$7+3+1=11$$

11 is not divisible by 9.

Option C: 729

$$7+2+9=18$$

Since 18 is divisible by 9, 729 is also divisible by 9.

$$729\div9=81$$

Option D: 742

$$7+4+2=13$$

13 is not divisible by 9.

Thus, only 729 satisfies the rule.

Correct Answer: C. 729

Question 5: Divisibility by Two Numbers

A number is divisible by both 4 and 6. Which of the following must divide that number?

A. 8

B. 12

C. 18

D. 24

Answer: B. 12

Concept: Least common multiple (LCM) and divisibility.

Explanation:

If a number is divisible by both 4 and 6, it must be divisible by their least common multiple.

The multiples of 4 are:

$$4,\ 8,\ 12,\ 16,\ 20,\ 24,\ldots$$

The multiples of 6 are:

$$6,\ 12,\ 18,\ 24,\ 30,\ldots$$

The smallest positive common multiple is 12.

Therefore:

$$\operatorname{LCM}(4,6)=12$$

Any number divisible by both 4 and 6 must be divisible by 12.

It does not necessarily have to be divisible by 24, as 12 itself is divisible by both 4 and 6 but not by 24.

Correct Answer: B. 12

Important Formulas & Concepts

Divisibility by 2

A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.

Divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

Divisibility by 4

A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Divisibility by 5

A number is divisible by 5 if its last digit is 0 or 5.

Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Factors and Multiples

If:

$$N=k\times m$$

then (N) is a multiple of (k), and (k) is a factor of (N).

Addition of Multiples

If:

$$A=ka,\qquad B=kb$$

then:

$$A+B=k(a+b)$$

Therefore, the sum is divisible by (k).

Least Common Multiple

If a number is divisible by two positive integers, it is divisible by their least common multiple.

Related Practice Questions

Try solving these questions independently.

1. Is 936 divisible by 3? Explain using the digit-sum rule.
2. Find the smallest positive number divisible by both 8 and 12.
3. Is 1,248 divisible by 4? Explain your answer.
4. Write three multiples of 7 greater than 50.
5. If two numbers are divisible by 6, what can you say about their sum?

Mini Quiz Challenge

Question 1

Which of the following numbers is divisible by 3?

A. 124

B. 215

C. 462

D. 701

Answer: C. 462

Explanation:

The sum of the digits of 462 is:

$$4+6+2=12$$

Since 12 is divisible by 3, 462 is divisible by 3.

Question 2

Which statement is always true?

A. The sum of two odd numbers is odd.

B. The product of an even number and any integer is even.

C. Every multiple of 5 is odd.

D. Every number divisible by 3 is divisible by 9.

Answer: B. The product of an even number and any integer is even.

Explanation:

An even number can be written as (2a). Multiplying it by an integer (b) gives:

$$2a\times b=2(ab)$$

The product has a factor of 2 and is therefore even.

Question 3

Which number is a common multiple of both 5 and 8?

A. 20

B. 30

C. 40

D. 45

Answer: C. 40

Explanation:

$$40=5\times8$$

It is divisible by both 5 and 8. Therefore, 40 is a common multiple.

Exam Tips

• Learn the divisibility rules for 2, 3, 4, 5, 8, 9, 10, and 11.
• Remember that every factor of a number divides it exactly.
• Check the digit sum carefully when using the rules for 3 and 9.
• Do not confuse a factor with a multiple.
• When a question involves two divisors, consider their LCM.
• Verify calculations before selecting an answer.

Quick Revision Notes

• Even numbers are divisible by 2.
• The digit-sum rule helps test divisibility by 3 and 9.
• A factor divides a number exactly.
• A multiple is obtained by multiplying a number by an integer.
• The sum of two multiples of the same number is also a multiple of that number.
• A number divisible by two integers is divisible by their LCM.

Common Mistakes Students Make

• Confusing factors with multiples.
• Applying the divisibility rule for 3 when the question asks about 9.
• Forgetting to calculate the complete digit sum.
• Assuming that a number divisible by 4 and 6 must always be divisible by 24.
• Making arithmetic errors when adding or subtracting integers.
• Choosing an answer without checking whether it satisfies the condition.

Key Takeaways

Number Play develops a deeper understanding of number patterns, divisibility, factors, multiples, and parity. Divisibility rules help simplify calculations, while the properties of multiples and common factors help students reason about numbers systematically.

Practising these concepts regularly can improve accuracy and confidence in mathematics.

FAQs

1. What is Chapter 5 of the new NCERT Class 8 Maths book?

Chapter 5 of Ganita Prakash, Part I is titled Number Play.

2. How can we check whether a number is divisible by 9?

Add all its digits. If their sum is divisible by 9, the original number is also divisible by 9.

3. What is the difference between a factor and a multiple?

A factor divides a number exactly, while a multiple is obtained by multiplying a number by an integer.

4. What happens when two multiples of the same number are added?

Their sum is also a multiple of that number.

5. Why is the LCM useful in divisibility problems?

The least common multiple identifies the smallest positive number divisible by two or more given positive integers.

Conclusion

This practice set covers fundamental concepts from Class 8 Mathematics Chapter 5, Number Play, including divisibility rules, factors, multiples, parity, and LCM. The detailed explanations help students understand the reasoning behind each answer rather than memorising rules alone.

Continue practising the upcoming sets to strengthen your number sense and mathematical reasoning.

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