check wheather 4 power 'n' will end with digit zero
Answers
#if 4 ^n for any n were to end with 0 must be divisible by 2 and 5.
#i.e. it must have the factors 2 and 5.
#but 4^n= (2)^2n.
#by the uniqueness of fundamental theorem of arithmetic no other no. other than 2 can be the factor of 4^n , for any n.
therefore 4^n cannot e.g. end with 0 for any natural number n.
Firstly,let us clear some terms
★Factorization:
The expression of number of numbers in terms of their multiples or factors
★Prime Factorization:
Expression of numbers in terms of their primes
E.g., 10=2×5
★Prime number:
A number which has only one and itself as a factor is a Prime Number
A concept used in solving the question,
If a number has 5 in its prime factorization,it is likely to end with zero
METHOD 1:
2 MARKS
Now,
Checking for 4ⁿ whether it will end with zero for any value positive value of n
Putting n=1,
4¹=4
Putting n=2,
4²=16
Putting n=3,
4³=64
Thus,it wouldn't end with zero for any value of n
METHOD 2:
1 MARKS
Prime factorization of,
4ⁿ
=2²ⁿ
As,it doesn't have 5 in its prime factorization,it wouldn't end with zero for any zero of n.
^_^