#### Question

Consider the number 12^{n} where n is a natural number. Check whether there is any value of n ∈ N for which 12^{n} ends with the digital zero.

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#### Solution

We know if any number ends with the digit zero it is always divisible by 5.

If 12^{n} ends with the digit zero, it must divisible by 5.

This is possible only if prime factorisation of 12^{n} contains the prime number 5.

Now, 12 = 2 x 2 x 3 = 2^{2} x 3

⇒ 12^{n} = (2^{2} x 3)^{n} = 2^{2n} x 3^{n}

i.e., prime factorisation of 12^{n} does not contain the prime number 5.

⇒ There is no value of n ∈ N for which 12^{n} ends with the digit zero.

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Solution for question: Consider the number 12^n where n is a natural number. Check whether there is any value of n ∈ N for which 12^n ends with the digital zero. concept: Fundamental Theorem of Arithmetic. For the course CBSE