## RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.3

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.3

Other Exercises

- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.1
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.2
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.3
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.4
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.5
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.6
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers VSAQS
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers MCQS

Question 1.

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

= 2^{2} x 3 x 5 x 7

Question 2.

Determine the prime factorization of each of the following positive integer :

(i) 20570

(ii) 58500

(iii) 45470971

Solution:

(i) 20570

20570 = 2 x 5 x 11 x 11 x 17 = 2 x 5 x 11^{2} 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 that number which can be factorize. 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 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 6^{n} can end with the digit 0 for any natural number n.

Solution:

No, 6^{n} can’t end with the digit 0 as the number ending 0 can be factorise of the type

2^{n} x 5^{m} only but 6^{n} = (2 x 3)^{n} = 2^{n} x 3^{n}

Which does not has 5^{m} as factors.

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 = 2^{4} 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.

Hope given RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.3 are helpful to complete your math homework.

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