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Solution - 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. - CBSE Class 10 - Mathematics

Question

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

Solution

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

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

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

Now, 12 = 2 x 2 x 3 = 22 x 3

⇒ 12n = (22 x 3)n = 22n x 3n

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

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

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Reference Material

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
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