Show that 12n cannot end with the digit 0 or 5 for any natural number n
Solution:
If any number ends with the digit 0 or 5, it is divisible by 5.
If 12n ends with the digit zero or five it should be divisible by 5.
It is possible if prime factorisation of 12n has the prime number 5.
12 = 2 × 2 × 3 = 22 × 3
12n = (22 × 3)n = 22n × 3n
Since, there is no term containing 5.
Therefore, there is no value of n ∈ N for which 12n ends with the digit zero or five
✦ Try This: Show that 9n cannot end with the digit 0 or 5 for any natural number n
If any number ends with the digit 0 or 5, it is always divisible by 5.
If 9n ends with the digit zero or five it must be divisible by 5.
This is possible only if prime factorisation of
9n contains the prime number 5.
Now, 9 = 3 × 3
9n = (3 × 3)n = 3n × 3n
Since, there is no term containing 5
Therefore, there is no value of n ∈ N for which 9n ends with the digit zero or five
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1
NCERT Exemplar Class 10 Maths Exercise 1.3 Problem 11
Show that 12n cannot end with the digit 0 or 5 for any natural number n
Summary:
12n cannot end with the digit 0 or 5 for any natural number n. Hence proved
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