Prime Factorisation

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

Has the prime factorisation been done in the following expression?

$70=2\times 5\times 7$

Has the prime factorisation been done in the following expression?

$56=7\times 2\times 2\times 2$

Has the prime factorisation been done in the following expression?

$24=2\times 3\times 4$

Which factors (other than the number itself) are not included in the prime factorization of a composite number?

Here, the factor tree for $60$ is given. Write the sum of missing numbers.

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

Determine if $25110$ is divisible by $45.$

Has the prime factorisation been done in the following expression?

$54=2\times 3\times 9$

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

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

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

Write the smallest $5$-digit number and express it in terms of its prime factors.

Write the greatest $4$-digit number and express it in terms of its prime factors.