Given an example of a number which is divisible by

Question:

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 by 32.

Solution:

(i) 10
Every number with the structure (4n + 2) is an example of a number that is divisible by 2 but not by 4.

(ii) 15
Every number with the structure (6n + 3) is an example of a number that is divisible by 3 but not by 6.

(iii) 28
Every number with the structure (8n + 4) is an example of a number that is divisible by 4 but not by 8.

(iv) 8
Every number with the  structure (32n + 8), (32n + 16) or (32n + 24) is an example of a number that is divisible by 4 and 8 but not by 32.

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