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1. Real Numbers
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Q5 of 18 Page 11

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

If any number has last digit 0,


Then, it should be divisible by 10


Factors of 10 = 2×5


So,


Value 6n should be divisible by 2 or 5


Prime factorisation of 6n = (2×3)n


Hence,


6n is divisible by 2 but not by 5.


It can not end with 0.


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3

Find the LCM and HCF of the following integers by applying the prime factorisation method.

(i) 12, 15 and 21


(ii) 17, 23 and 29


(iii) 8, 9 and 25

4

Given that HCF (306, 657) = 9, find LCM (306, 657).

6

Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

7

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the

same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Questions · 18
1. Real Numbers
1 2 3 4 5 1 2 3 4 5 6 7 1 2 3 1 2 3
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