Show that any number of the form 4n, n ∈ N
Question:

Show that any number of the form 4nn ∈ N can never end with the digit 0.

 

Solution:

If 4n ends with 0, then it must have 5 as a factor.
But we know the only prime factor of 4n is 2.
Also we know from the fundamental theorem of arithmetic that prime factorisation of each number is unique.
Hence, 4n can never end with the digit 0.

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