Home » MCQ on Class 10 Mathematics Chapter 1: Real Numbers

MCQ on Class 10 Mathematics Chapter 1: Real Numbers

By Abdur Rohman / July 2, 2024

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Chapter 1 of class 10 Mathematics as per the NCERT syllabus is Real Numbers which deals with Euclid’s division algorithm and the Fundamental Theorem of Arithmetic and discusses their applications, including finding the highest common factor (HCF) and least common multiple (LCM) of numbers, and proving the irrationality of certain numbers.

Here, we have discussed 30 Multiple Choice Questions based on these topics of the chapter. These questions will help you to learn more about the chapter and test your knowledge.

For each question below, there are four options out of which only one option is correct. After selecting your answer, click on the submit button to see the score and review your answers.

MCQ on Class 10 Maths Chapter 1 Real Numbers

1. What is the Fundamental Theorem of Arithmetic?

A. Every number can be expressed as a sum of primes B. Every prime number can be written as a product of other primes C. Every composite number can be expressed as a product of primes D. Every prime number can be expressed as a product of composite numbers

2. What does Euclid’s division algorithm state?

A. Every integer can be divided by any other integer without remainder B. Any positive integer can be divided by another positive integer to leave a remainder smaller than the divisor C. Every number can be divided into two equal parts D. Any negative integer can be divided by another negative integer to leave a remainder smaller than the divisor

3. What is the result of 32760 expressed as a product of its prime factors?

A. \(2^3 \times 3^2 \times 5 \times 7 \times 13\) B. \(2^4 \times 3^2 \times 5 \times 7 \times 13\) C. \(2^3 \times 3 \times 5 \times 7 \times 13\) D. \(2^3 \times 3^2 \times 5 \times 7^2 \times 13\)

4. Which mathematician gave the first correct proof of the Fundamental Theorem of Arithmetic?

A. Euclid B. Pythagoras C. Carl Friedrich Gauss D. Isaac Newton

5. What is the prime factorization of 123456789?

A. \(3^2 \times 3803 \times 3601\) B. \(3 \times 3803 \times 3607\) C. \(3^2 \times 3801 \times 3607\) D. \(3^2 \times 3803 \times 3607\)

6. Which of the following numbers is irrational?

A. \(4\) B. \(\sqrt{3}\) C. \(1.5\) D. \(2.25\)

7. What does the Fundamental Theorem of Arithmetic guarantee about the factorization of a composite number?

A. It can be factorized in multiple unique ways B. It can be factorized in only one unique way C. It cannot be factorized at all D. It can be factorized in a non-unique way

8. What is the HCF of 6 and 20 using the prime factorization method?

A. \(4\) B. \(2\) C. \(6\) D. \(1\)

9. What is the LCM of 6 and 20 using the prime factorization method?

A. \(60\) B. \(30\) C. \(120\) D. \(40\)

10. What does HCF(6, 20) × LCM(6, 20) equal?

A. \(80\) B. \(120\) C. \(100\) D. \(40\)

11. What is the HCF of 96 and 404 using the prime factorization method?

A. \(4\) B. \(8\) C. \(2\) D. \(1\)

12. What is the LCM of 96 and 404 using the prime factorization method?

A. \(9696\) B. \(4800\) C. \(9696\) D. \(4840\)

13. What is the prime factorization of \(n^2 – 1\) when \(n\) is an odd integer?

A. \((n-1)^2(n+1)^2\) B. \((n-1)^2(n+1)\) C. \((n-1)(n+1)\) D. \((n-1)(n+1)^2\)

14. What is the HCF of two co-prime numbers?

A. \(1\) B. \(0\) C. The product of the two numbers D. The sum of the two numbers

15. Which of the following numbers is a rational number?

A. \(\sqrt{2}\) B. \(\frac{4}{5}\) C. \(\pi\) D. \(e\)

16. If \(a = 2^2 \times 3 \times 5\) and \(b = 2 \times 3^3 \times 5^2\), what is the HCF(a, b)?

A. \(2 \times 3 \times 5\) B. \(2 \times 3 \times 5^2\) C. \(2^2 \times 3^3 \times 5\) D. \(2^2 \times 3^3 \times 5^2\)

17. If \(a = 2^2 \times 3 \times 5\) and \(b = 2 \times 3^3 \times 5^2\), what is the LCM(a, b)?

A. \(2^2 \times 3^3 \times 5\) B. \(2 \times 3 \times 5\) C. \(2^2 \times 3^3 \times 5^2\) D. \(2 \times 3 \times 5^2\)

18. The product of two positive integers is equal to the product of their HCF and LCM. True or False?

A. True B. False

19. What is the product of the HCF and LCM of two numbers a and b if \(a = 14\) and \(b = 28\)?

A. \(28\) B. \(392\) C. \(14\) D. \(196\)

20. If two numbers are co-prime, what is their LCM?

A. The sum of the numbers B. The difference of the numbers C. 1 D. The product of the numbers

21. If \(a\) and \(b\) are two positive integers such that \(a = 12\) and \(b = 18\), what is the LCM(a, b)?

A. \(6\) B. \(36\) C. \(72\) D. \(54\)

22. If \(a\) and \(b\) are two positive integers such that \(a = 12\) and \(b = 18\), what is the HCF(a, b)?

A. \(12\) B. \(6\) C. \(36\) D. \(3\)

23. If \(a = p_1^{a_1} \times p_2^{a_2} \times … \times p_n^{a_n}\) and \(b = p_1^{b_1} \times p_2^{b_2} \times … \times p_n^{b_n}\), what is the LCM(a, b)?

A. \(p_1^{a_1} \times p_2^{a_2} \times … \times p_n^{b_n}\) B. \(p_1^{b_1} \times p_2^{b_2} \times … \times p_n^{a_n}\) C. \(p_1^{\max(a_1, b_1)} \times p_2^{\max(a_2, b_2)} \times … \times p_n^{\max(a_n, b_n)}\) D. \(p_1^{\min(a_1, b_1)} \times p_2^{\min(a_2, b_2)} \times … \times p_n^{\min(a_n, b_n)}\)

24. If \(a = p_1^{a_1} \times p_2^{a_2} \times … \times p_n^{a_n}\) and \(b = p_1^{b_1} \times p_2^{b_2} \times … \times p_n^{b_n}\), what is the HCF(a, b)?

A. \(p_1^{a_1} \times p_2^{a_2} \times … \times p_n^{b_n}\) B. \(p_1^{b_1} \times p_2^{b_2} \times … \times p_n^{a_n}\) C. \(p_1^{\min(a_1, b_1)} \times p_2^{\min(a_2, b_2)} \times … \times p_n^{\min(a_n, b_n)}\) D. \(p_1^{\max(a_1, b_1)} \times p_2^{\max(a_2, b_2)} \times … \times p_n^{\max(a_n, b_n)}\)

25. The HCF and LCM of two numbers are 4 and 24, respectively. If one of the numbers is 12, what is the other number?

A. \(4\) B. \(8\) C. \(12\) D. \(16\)

26. The prime factorization of 210 is:

A. \(2 \times 3 \times 5 \times 7\) B. \(2 \times 3 \times 5 \times 7\) C. \(2^2 \times 3 \times 5 \times 7\) D. \(2 \times 3 \times 5^2 \times 7\)

27. Which of the following is a co-prime pair?

A. \(12, 15\) B. \(14, 21\) C. \(14, 15\) D. \(18, 24\)

28. What is the decimal expansion of an irrational number?

A. Terminating B. Non-terminating and repeating C. Non-terminating and non-repeating D. Repeating

29. Which of the following is an example of an irrational number?

A. \(\pi\) B. \(3.14\) C. \(\frac{22}{7}\) D. \(1.5\)

30. Which of the following is the smallest prime number?

A. \(1\) B. \(3\) C. \(4\) D. \(2\)

Review Your Answers Above.

The Bottom Line

I hope these 30 MCQs on Real Numbers of Class 10 Maths Chapter 1 have helped you in your studies and preparation.

If you have any queries, or comments or find any mistake in the above questions, feel free to contact me in the comment section below.

I would love to hear from you.

Abdur Rohman

Abdur Rohman is an Electrical Engineer from Charaideo, Assam, who wears multiple hats as a part-time teacher, blogger, entrepreneur, and digital marketer. Passionate about education, he founded The Assam School blog to provide free, comprehensive textbook solutions, MCQs (Multiple Choice Questions), and other academic content for students from Class V to XII.