ANSWER:

Divisibility of numbers by 2:

A number that has 0, 2, 4, 6 or 8 in its ONES place is divisible by 2.

Divisibility of numbers by 3:

A number is divisible by 3 if the sum of its digits is divisible by 3.

Divisibility of numbers by 4:

A number is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.

Divisibility of numbers by 5:

A number that has either 0 or 5 in its ones place is divisible by 5.

Divisibility of numbers by 6:

A number is divisible by 6 if that number is divisible by both 2 and 3

Divisibility of numbers by 8:

A number is divisible by 8 if the number formed by its last three digits (i.e. ones, tens and hundreds) is divisible by 8.

Divisibility of numbers by 9:

A number is divisible by 9 if the sum of its digits is divisible by 9.

Divisibility of numbers by 10:

A number that has 0 in its ones place is divisible by 10.

Divisibility of numbers by 11:

If the difference between the sum of the digits at the odd and even places in a given number is either 0 or a multiple of 11, then the given number is divisible by 11.

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Solution:

a)

FALSE

Because there are many numbers which are divisible by 3 but not divisible by 9.

For e.g

15 is divisible by 3 but not divisible by 9.

b)

TRUE

Because if a number is divisible by any number then it is divisible by each factor of that number .

Here 3 is a factor of 9.

For e.g

27/9= 3, & 27/3= 9

c)

FALSE

For e.g

Number 30 is divisible by 3 and 6 both but not divisible by 18.

d)

TRUE

Because if a number is divisible by 2 coprime numbers then it is divisible by their product ALSO.

e)

FALSE

We know that two prime numbers having only one as a common factor are called co- prime numbers so it is not necessary that one of them must be Prime.

For e.g

8 and 15 are coprime numbers since both have only 1 as a common factor but no one is a prime number.

f)

FALSE

For e.g

36 is divisible by 4 but not divisible by 8.

g)

TRUE

If a number is divisible by any number then it is divisible by each factor of that number .

Here 4 is a factor of 8 so all the number divisible by 8 must also be divisible by 4.

For e.g

56 is divisible by 8 as well divisible by 4.

h)

TRUE

If two given numbers are divisible by a number then their sum is also divisible by that number.