RD Chapter 1- Real Numbers Ex-1.1 |
RD Chapter 1- Real Numbers Ex-1.2 |
RD Chapter 1- Real Numbers Ex-1.4 |
RD Chapter 1- Real Numbers Ex-1.5 |
RD Chapter 1- Real Numbers Ex-1.6 |
RD Chapter 1- Real Numbers Ex-VSAQS |
RD Chapter 1- Real Numbers Ex-MCQS |

Express each of the following integers as a product of its prime factors :

(i) 420

(ii) 468

(iii) 945

(iv) 7325

**Answer
1** :

(i) 420

=2 x 2 x 3 x 5 x 7

= 22 x 3 x 5 x 7

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

(i) 20570

(ii) 58500

(iii) 45470971

**Answer
2** :

(i) 20570

20570 = 2 x 5 x 11 x 11 x 17 = 2 x 5 x 112 x 17

**Answer
3** :

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

**Answer
4** :

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

2^{n} x 5^{m} onlybut 6^{n} = (2 x 3)^{n} = 2^{n} x3^{n}

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

**Answer
5** :

We have, 3 x 5 x 7 + 7 = 105 + 7 = 112

Now, 112 = 2 x 2 x 2 x 2 x 7 = 2^{4} x7

So, it is the product of prime factors 2 and 7. i.e., it has more than twofactors.

Hence, it is a composite number.

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