Question

Check whether 18^n can end with the digit zero for any natural number

Answer 1

Answer:

No

Step-by-step explanation:

for number 18 ^ 2 to end with 0 for any natural number , it should be divisible by 2 and 5 .this means that the prime factorization of 18 ^ n should contain the prime numbers 2 and 5 but it is not possible because 18 ^ n is equal to 2 into 3 ^ 2 .so, 2 and 3 e are the only prime number in the factorization of 18 ^ n ,Since 5 is not present in the prime factorization of 18 ^ n there is no natural number for which 18 ^ n end with the digit 0 .

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Answer 2

Answer:

Let us think of some numbers which end the digit 0

10 = 5 × 2

100 = 2 × 2 × 5 × 5

Many more...

Now, Clearly we can see that numbers ending with 0 has prime factors as 2 and 5, take any number ending with digit 0 , it will do have 2 and 5 as a factor.

But,

8^n = (4 × 2) ^n

It doesn't have 5 as it's factor thus 8^n cannot end with zero for any natural number n.