Question

Show that 5^n can never end with digit 0​

Answer 1

Let 5^n ends with the digit 0.

Therefore 2 and 5 are the only prime factors of 5^n.

But 5^n=(1x5)^n

=> 5 and 1 are the only prime factors of 5^n.

Therefore our assumption is false

Therefore 5^n can never end with the digit 0.

Hope it is helpful for you.

Answer 2

Step-by-step explanation:

In $5^{n}$ ends with 0 then it must have 5  as a factor.

But, $5^{n}$ show that 5 is the only prime factors of $5^{n}$.

Also we know from the fundamental theorem of arithmetic that the prime factorization of each number is unique.

So, 5 is  a factor of $5^{n}$ .

Hence, $5^{n}$ can end with the digit 0.

So the above statement is wrong