Question

Show that number 8n can never end with digit 0 for any integer number n.

Answer 1

If 8ⁿ is end with Zero then it must have factor 2ⁿ × 5 ^m

But 6 has ( 2 × 3 )ⁿ as a factor

So ,

By the fundamental theorem of Algorithm the prime factorisation of each number is unique.

There fore , 6ⁿ can never be end with Zero.

Answer 2

For ending with 0 the number should have prime factorisation as 2ⁿ × 5^m.

But 8ⁿ has prime factorisation as 2³ⁿ

So it can't be end with 0