check whether 20^n can end with the digit 5 for any natural number n
Answers
Answer:
Step-by-step explanation:
= 20ⁿ
= ( 5 x 4 )ⁿ
= 5ⁿ x 4ⁿ
To end with the digit 5 any number should be in the form of either 5^m x 3^n or 5^m x 7^n ( Where m and n are whole numbers ).But here it is not so.
Hence 20ⁿ can't end with 0.
Given,
Number =
To Find,
Whether can end with the digit 5 for any natural number n =?
Solution,
We have to find whether the one place digit of can be equal to 5 or not.
From factorization of 20 = 2*2*5
We know that, for the last place to be 5, 5 should be multiplied by an odd number, then only the last digit is 5 such as 5*3 = 15, 5*5 = 25.
But in 20 there is no odd number except 5. Whenever 5 is multiplied by 2 or multiples of 2, we get 0 as the last place digit.
As we can see, for no value of n can end with digit 5.
Hence, can never end with the digit 5 for any natural number n.