Question

Show that 12n can never end with the digit zero for any

natural number n.​

Answer 1

Step-by-step explanation:

If any number ends with the digit 0 or 5, it is always divisible by 5.

If 12n ends with the digit zero it must be divisible by 5.

This is possible only if prime factorisation of 12n contains the prime number 5.

This is possible only if prime factorisation of 12n contains the prime number 5.

Now, 12 = 2 × 2 × 3 = 22 × 3

⇒ 12n = (22 × 3)n = 22n × 3n [since, there is no term contains 5]

Hence, there is no value of n e N for which 12n ends with digit zero or five.