NCERT Solutions for Class 10 Maths Chapter 1 – Real Number Exercise 1.2

NCERT Solutions Class 10 Maths Chapter 1 – Real Numbers Exercise 1.2 are provided here to help students in their Class 10 exam preparations. These solutions are prepared by our subject experts to ensure that students understand Euclid's Division Algorithm and the divisibility of integers clearly. Each solution is explained step-by-step, ensuring easy comprehension of the concepts while solving the problems in the exercise.

Exercise 1.2 in Real Numbers is focused on using Euclid's Division Algorithm to solve problems related to divisibility and finding the greatest common divisor (gcd). The NCERT solutions provided here cover the problems in a logical and clear manner, ensuring that students can apply the algorithm effectively and build strong problem-solving skills.

NCERT Solutions for Class 10 Maths Chapter 1 – Real Number Exercise 1.2

Real Numbers
Medium
Q.
Express each number as a product of its prime factors:
(i) 140  (ii) 156  (iii) 3825  (iv) 5005  (v) 7429
Real Numbers
Medium
Q.
Find the LCM and HCF of the following pairs of integers and verify that
LCM × HCF = product of the two numbers.
(i)   26 and 91
(ii)  510 and 92
(iii) 336 and 54
Real Numbers
Easy
Q.
If HCF(98, 28) = m and LCM(98, 28) = n, then the value of n – 7m is:
[CBSE - 2025]
Real Numbers
Easy
Q.
If two positive integers p and q can be expressed as p=18 a2b4\rm p = 18\ a^2b^4​ and q=20 a3b2\rm q = 20\ a^3b^2​, where a and b are prime numbers, then LCM(p, q) is:
[CBSE - 2024]
Real Numbers
Easy
Q.
Find the HCF of 1260 and 7344 using Euclid's algorithm.
[CBSE - 2023]

NCERT Solutions for Class 10 Maths Chapter 1 – Real Number Exercise 1.2

These solutions are designed according to the latest CBSE syllabus, making them perfect for exam preparation. By practicing these solutions, students will be able to score better in their exams and understand the applications of Euclid’s Division Algorithm.

  • Question:
    Express each number as a product of its prime factors:
    (i) 140
    (ii) 156
    (iii) 3825
    (iv) 5005
    (v) 7429

    Answer:

    • (i) 140 = 2 × 2 × 5 × 7

    • (ii) 156 = 2 × 2 × 3 × 13

    • (iii) 3825 = 3 × 5 × 5 × 7 × 11

    • (iv) 5005 = 5 × 7 × 11 × 13

    • (v) 7429 = 7429 (already prime)

    View Solution

  • Question:
    Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers:
    (i) 26 and 91
    (ii) 510 and 92
    (iii) 336 and 54

    Answer:

    • (i) LCM(26, 91) = 182, HCF(26, 91) = 13

    • (ii) LCM(510, 92) = 4680, HCF(510, 92) = 2

    • (iii) LCM(336, 54) = 1512, HCF(336, 54) = 18

    Verification:

    • LCM × HCF = product of the numbers:

      • For (i): 182 × 13 = 26 × 91

      • For (ii): 4680 × 2 = 510 × 92

      • For (iii): 1512 × 18 = 336 × 54

    View Solution

  • Question:
    If HCF(98, 28) = m and LCM(98, 28) = n, then the value of n – 7m is:

    Answer:

    • HCF(98, 28) = 14, LCM(98, 28) = 196

    • Therefore, n – 7m = 196 – 7(14) = 196 – 98 = 98

    View Solution

  • Question:
    If two positive integers p and q can be expressed as:
    p=18a2b4p = 18a^2b^4
    q=20a3b2q = 20a^3b^2
    where a and b are prime numbers, then LCM(p, q) is:

    Answer:
    The LCM of two numbers is the product of the highest powers of all prime factors involved.

    • LCM(p, q) = 22×32×5×a3×b42^2 \times 3^2 \times 5 \times a^3 \times b^4

    View Solution

  • Question:
    Find the HCF of 1260 and 7344 using Euclid's algorithm:

    Answer:
    Using Euclid’s algorithm, we can repeatedly subtract the smaller number from the larger number until we get the remainder as 0:

    • 7344 ÷ 1260 = 5, remainder = 744

    • 1260 ÷ 744 = 1, remainder = 516

    • 744 ÷ 516 = 1, remainder = 228

    • 516 ÷ 228 = 2, remainder = 60

    • 228 ÷ 60 = 3, remainder = 48

    • 60 ÷ 48 = 1, remainder = 12

    • 48 ÷ 12 = 4, remainder = 0
      Hence, HCF = 12

    View Solution

FAQs: Class 10 Maths Chapter 1 – Real Numbers Exercise 1.2

Q1. What is the main concept covered in Exercise 1.2?
Answer:
Exercise 1.2 focuses on Euclid's Division Algorithm to solve problems involving divisibility and finding the greatest common divisor (gcd) of two numbers.

Q2. How do I apply Euclid's Division Algorithm?
Answer:
Euclid's Division Algorithm involves dividing a number a by another number b, and expressing the division as:
a = b × q + r,
where a is the dividend, b is the divisor, q is the quotient, and r is the remainder. The remainder r must be less than b (i.e., 0 ≤ r < b).

Q3. How does solving Exercise 1.2 help with understanding the gcd?
Answer:
By solving the problems in this exercise, you will learn how to find the gcd of two numbers using Euclid's Division Algorithm. This is an essential concept in number theory and has practical applications in simplifying fractions and solving problems in algebra.

Q4. What is the importance of Euclid's Division Algorithm?
Answer:
Euclid's Division Algorithm is fundamental for finding the greatest common divisor of two numbers. It forms the basis for many number-theoretic concepts and is also used in finding lcm (least common multiple) and simplifying algebraic expressions.

Q5. How do NCERT Solutions for Exercise 1.2 help with exam preparation?
Answer:
These solutions provide step-by-step guidance, helping you understand how to apply Euclid’s Division Algorithm correctly and practice the problem-solving techniques needed for exams. They are structured to enhance your understanding and help you achieve better marks in board exams.