PDF chapter test TRY NOW

1. Check whether 6^n can end with the digit 0 for any natural number n.
 
Solution:
 
The number, which ends with digit 0, must be a multiple of 10.
 
The prime factor of 10 is 2 \times 5.
 
That means, if a number ends with digit 0, then it must contain 2 and 5 as the factors.
 
Now, 6^n = (2 \times 3)^n.
 
Here, 6^n contains 2 as a factor, but it does not contain the factor 5.
 
So, it does not end with the digit 0.
 
Therefore, 6^n cannot end with the digit 0 for any natural number n.
 
 
2. Find the LCM and HCF of 15 and 42 by the prime factorisation method. Also, find their product.
 
Solution:
 
First, let us write the given numbers as a product of primes.
 
15 = 3 \times 5
 
42 = 2 \times 3 \times 7
 
LCM = 2 \times 3 \times 5 \times 7 = 210
 
HCF = 3
 
HCF \times LCM = 210 \times 3 = 630
 
Note from the above example:
 
HCF \times LCM = 630
 
We know, 15 \times 42 = 630.
 
So, HCF \times LCM = 15 \times 42
 
That is, HCF \times LCM = Product of the given numbers.
 
Important!
For any two positive integers a and b:
  
HCF (a, b) \times LCM (a, b) = a \times b