Question

show that the number of the form 5^n, n€N cannot have unit digit zero​

Answer 1

According to the fundamental theorem of arithmetic, any number with 2^n*5^n

in its denominator has 0 in the unit place.

If any number ends with the digit 0, it should be divisible by 10 or in other words, it will also be divisible by 2 and 5 as 10 = 2 × 5 It can be observed that 2 is not in the prime factorisation of 5n.

Hence, for any value of n, 5n will not be divisible by 2.

Therefore, 5n cannot end with the digit 0 for any natural number n.

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