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Solution - Check whether 6n can end with the digit 0 for any natural number n. - CBSE Class 10 - Mathematics

ConceptFundamental Theorem of Arithmetic

Question

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

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.

Is there an error in this question or solution?

APPEARS IN

NCERT Mathematics Textbook for Class 10
Chapter 1: Real Numbers
Q: 5 | Page no. 11

Reference Material

Solution for question: Check whether 6n can end with the digit 0 for any natural number n. concept: Fundamental Theorem of Arithmetic. For the course CBSE
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