Check the number 4^n, where n is a natural number. Check whether there is any value of n for which 4^n ends with digit zero.
Answers
Answer:
Not possible!
Step-by-step explanation:
Method - 1:
Let us take the example of a number which ends with digit 0.
So, 10 = 2 * 5
Here, we note that numbers ending with 0 has both 2 and 5 as factors.
Whereas, 4ⁿ = (2 * 2)ⁿ
It does not have 5 as their prime factor.
So,it does not end with zero.
Therefore, 6ⁿ cannot end with zero for any natural number n.
Method - 2:
Prime factorization of 4ⁿ = (2 * 2)ⁿ
It can be observed that 5 is not in the prime factorization of of 4ⁿ.
Hence, there is no natural number n for which 4ⁿ ends with the digit zero.
Hope it helps!
Step-by-step explanation:
Prime factorization of 4ⁿ = (2 * 2)ⁿ
It can be observed that 5 is not in the prime factorization of of 4ⁿ.
Hence, there is no natural number n for which 4ⁿ ends with the digit zero.