Given an example of a number which is divisible by
(i) 2 but not by 4.
(ii) 3 but not by 6.
(iii) 4 but not by 8.
(iv) both 4 and 8 but not 32.

To do:

We have to give an example of a number which is divisible by

(i) 2 but not by 4.

(ii) 3 but not by 6.

(iii) 4 but not by 8.

(iv) both 4 and 8 but not 32.

Solution:

(i) We know that,

A number is divisible by 2 if the units digit of it is even but it is divisible by 4 if the number formed by tens digit and ones digit is divisible by 4.

Therefore,

Numbers which are divisible by 2 but not by 4 are 14, 18, 122, 222, etc.

(ii) We know that,

A number is divisible by 3 if the sum of its digits is divisible by 3 but a number is divisible by 6, if it is divided by 2 and 3 both.

Therefore,

Numbers which are divisible by 3 but not by 6 are 9, 21, 123, 333, etc.

(iii) We know that,

A number is divisible by 4 if the number formed by the tens digit and ones digit is divisible by 4 but a number is divisible by 8, if the number formed by hundreds digit, tens digit and ones digit is divisible by 8.

Therefore,

Numbers which are divisible by 4 but not by 8 are 124, 244, 324, etc.

(iv) We know that,

A number is divisible by 8 if the number formed by hundreds digit, tens digit and ones digit is divisible by 8.

A number divisible by 8 is also divisible by 4.

A number which is divisible by both 4 and 8 is not necessarily divisible by 32.

Therefore,

Numbers which are divisible by both 4 and 8 but not by 32 are 152, 328, etc.

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Updated on: 10-Oct-2022

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