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Real Numbers

Question
CBSEENMA10006103
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Check whether 6n can end with the digit 0 for any natural number n

Solution

If the number 6n, for any natural number n, ends with digit 0, then it is divisible by 5. That is, the prime factorisation of 6n contains the prime 5. This is not possible because the primes in the factorisation of 6n are 2 and 3 and the uniqueness of the Fundamental Theorem of Arithmetic guarantees that there are no other primes in the factorisation of 6n.

So, there is no natural number n for which 6n ends with digit zero.

Some More Questions From Real Numbers Chapter

Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m + 8.

Express each number as a product of its prime factors: (i) 140 

Express each number as a product of its prime factors: (ii) 156 

Express each number as a product of its prime factors: (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

Express each number as a product of its prime factors: (iv) 5005 

Express each number as a product of its prime factors:  (v) 7429

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.  (ii) 510 and 92 

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.  (iii) 336 and 54

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