show that 3^n*4^m cannot end with the digit 0 or 5 for any natural number
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Answered by
116
4- 2x2
4^m - 2^2^m
if it end with 0 or 5 it should be a factor of5
therefore it won't end with zero
4^m - 2^2^m
if it end with 0 or 5 it should be a factor of5
therefore it won't end with zero
Answered by
95
Let us take example of a number ending with 0
10=2×5
100=2×2×5×5
Therefore, number ending with 0 has 2 and 5 as the only prime factors
Whereas, 3^n=(3×1)^n
It is not in form of 2^m×2^n
Therefore, 3^n cannot end with 0 or 5
Similarly,
4^n=(2×2)^n
5 is missing in prime factors of 4
Therefore, it cannot end with 0 or 5
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