Prove that there is no natural number for which 4n ends with the digit zero
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consider ,
4={2x2}^n
therefore we know that a digit can be end with zero if it has 5 as factor . since 4^n has not 5 as factor so it can not end with zero
4={2x2}^n
therefore we know that a digit can be end with zero if it has 5 as factor . since 4^n has not 5 as factor so it can not end with zero
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Step-by-step explanation:
→ No, 4ⁿ can never end with the digit 0 for any natural number n .
→ If 4ⁿ ends with 0 then it must have 5 as a factor .
But, 4ⁿ = ( 2² )ⁿ = 2²ⁿ .
→ It shows that 2 is the only prime factor of 4ⁿ .
Also, we know from the fundamental theorem of airthematic that the prime factorisation of each number is unique .
So, 5 is not a factor of 4ⁿ .
Hence, 4ⁿ can never end with the digit 0 .
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