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Check whether 6n can end with the digit 0 for any natural number n. - Mathematics

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Check whether 6n can end with the digit 0 for any natural number n.

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Solution

if the number 6n ends with the digital zero, then it is divisible by 5. Therefore the prime factorization of 6n contains the prime 5. This is not possible because the only prime in the factorisation of 6n is 2 and 3 the uniqueness of the fundamental theorem of arithematic guarantees that these are no other prime in the factorization of 6n.

Hence it is very clear that thereis novalue of n in natural numbers for which 6n ends with the digit zero.

Concept: Fundamental Theorem of Arithmetic
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APPEARS IN

NCERT Class 10 Maths
Chapter 1 Real Numbers
Exercise 1.2 | Q 5 | Page 11

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