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Question

Consider the number 4n, where n is a natural number. Check whether there is any value of n for which 4n ends with the digit zero. [2 MARKS]

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Solution

Concept : 1 Mark
Application : 1 Mark

If the number 4n, for any n, were to end with the digit zero, then it would be divisible by 5.

That is, the prime factorization of 4n would contain the prime 5.

But, 4n=(2×2)n

The only prime in the factorization of 4n is 2.

So, the uniqueness of the Fundamental Theorem of Arithmetic guarantees that there are no other primes in the factorization of 4n.

So, there is no natural number n for which 4n ends with the digit zero.


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