RD Sharma Class 10 Solutions Chapter 1 Exercise 1.3: Every composite number can be written as a product of primes, according to the Fundamental Theorem of Arithmetic. The questions in this exercise are solved using this concept. To assist students, the RD Sharma Solutions Class 10 is an excellent resource to use for quickly clarifying concerns and learning the correct process for solving problems. Use the RD Sharma Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.3 PDF, which is accessible below.
Download RD Sharma Class 10 Solutions Chapter 1 Exercise 1.3 Free PDF
RD Sharma Class 10 Solutions Chapter 1 Exercise 1.3 PDF
Access answers to RD Sharma Solutions Class 10 Maths Chapter 1 Exercise 1.3- Important Question with Answers
Express each of the following integers as a product of its prime factors :
(i) 420
(ii) 468
(iii) 945
(iv) 7325
Solution:
(i) 420
=2 x 2 x 3 x 5 x 7
= 22 x 3 x 5 x 7
Question 2.
Determine the prime factorization of each of the following positive integers:
(i) 20570
(ii) 58500
(iii) 45470971
Solution:
(i) 20570
20570 = 2 x 5 x 11 x 11 x 17 = 2 x 5 x 112 x 17
Question 3.
Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.
Solution:
We know that a composite number is a number that can be factorized. It has more factors other than itself and one
Now, 7 x 11 x 13 + 13 = 13 (7 x 11 + 1) = 13 x 78
Which is a composite number
Similarly,
7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 = 5(7 x 6 x 4 x 3 x 2 x 1 + 1)
= 5 x 1009
Which is a composite number
Hence proved
Question 4.
Check whether 6n can end with the digit 0 for any natural number n.
Solution:
No, 6n can’t end with the digit 0 as the number ending 0 can be factorized of the type
2n x 5m only but 6n = (2 x 3)n = 2n x 3n
Which does not has 5m as a factor.
Question 5.
Explain why 3 x 5 x 7 + 7 is a composite number. [NCERT Exemplar]
Solution:
We have, 3 x 5 x 7 + 7 = 105 + 7 = 112
Now, 112 = 2 x 2 x 2 x 2 x 7 = 24 x 7
So, it is the product of prime factors 2 and 7. i.e., it has more than two factors.
Hence, it is a composite number.
We have provided complete details of RD Sharma Class 10 Solutions Chapter 1 Exercise 1.3. If you have any queries related to CBSE Class 10, feel free to ask us in the comment section below.
FAQs on RD Sharma Class 10 Solutions Chapter 1 Exercise 1.3
Where can I download RD Sharma Class 10 Solutions Chapter 1 Exercise 1.3 free PDF?
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Is it required to remember all of the questions in Chapter 1 Exercise 1.3 of RD Sharma Solutions for Class 10 Maths?
Yes, all of the questions in RD Sharma Solutions for Class 10 Maths Chapter 1 Exercise 1.3 must be learned. These questions may appear on both board exams and class tests. Students will be prepared for their board exams if they learn these questions.
What are the benefits of using RD Sharma Class 10 Solutions Chapter 1 Exercise 1.3?
1. Correct answers according to the last CBSE guidelines and syllabus.
2. The solutions are written in simple language to assist students in their board examination, & competitive examination preparation.
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