# Exercise 3.5

Complete above steps to enable this content

60 | ||||||||

6 | × | 10 | ||||||

2 | × | 3 | 2 | × | 5 | |||

60 | = | 2 | × | 3 | × | 2 | × | 5 |

**Which factors are not included in the prime factorisation of a composite number?**

Determine the Prime factorization of numbers:

prime -

Composite - It has more than

Hence,

Complete above steps to enable this content

**And express it in terms of its prime factors**.

- The smallest 5-digit number is
. -
is even check with divisible by 10000 x . - This process will be continue until the number reaches divisible by 2.
- 625 is not divisible by 2 check with different number
. - continue until reaches 1.
- Thus, the prime factorization of 10000 is:

Complete above steps to enable this content

**Find all the prime factors of 1729 and arrange them in ascending order. Now state the relation, if any; between two consecutive prime factors.**

Complete above steps to enable this content

**The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.**

Complete above steps to enable this content

**7. The sum of two consecutive odd numbers is divisible by 4. Verify this statement with the help of some examples.**

Complete above steps to enable this content

**8. In which of the following expressions, prime factorisation has been done?**

Complete above steps to enable this content

**18 is divisible by both 2 and 3. It is also divisible by 2 × 3 = 6. Similarly, a number is divisible by both 4 and 6. Can we say that the number must also be divisible by 4 × 6 = 24? If not, give an example to justify your answer.**

Complete above steps to enable this content

**I am the smallest number, having four different prime factors. Can you find me.**