Question

Show that 12ⁿ cannot end with digit 0 or 5 for any natural number n *

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Answer 1

Answer: 12^n cannot end with digit 0 or 5

Step-by-step explanation:12^n has multiples= 2×2×3.

Since the multiples of 12 do not contain 5 therefore it cannot end with 0 or5

This is because if any no. Is ending with 5 then it must have atleast one 5 in its multiples and if any no. Ends with 0 then it must have a pair of 5&2 as its multiples

I hope it helps...!!

Answer 2

Answer:

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.

HOPE IT HELPS..

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