Show that any number of the form 4n- n - N can never end with the digit 0 -

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 p ...

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Standard X

Mathematics

Fundamental Theorem of Arithmetic

Show that any...

Question

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

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

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.

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

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.