Consider the numbers 4n , where n is a natural number. Check whether there is any value of n for which 4n ends with the digit zero.

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Consider the numbers 4n , where n is a natural number. Check whether there is any value of n for which 4n  ends with the digit zero.

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Understand the Problem: Understand the problem. We need to determine if there is a natural number n such that when multiplied by 4, the product ends with the digit zero.Analyze Number Properties: Analyze the properties of numbers ending with zero. A number ends with the digit zero if it is a multiple of 10. This means that the number must have 2 and 5 as factors.Prime Factorization of 4: Consider the prime factorization of 4. The number 4 is 2^2 in prime factorization. It has the factor 2 but lacks the factor 5.Introducing Factor 5: Determine if multiplying 4 by a natural number n can introduce the factor 5. Since 4 does not contain the factor 5, multiplying it by any natural number n will not introduce the factor 5 unless n itself contains the factor 5.Check for Multiple of 5: Check if n can be a multiple of 5. If n is a multiple of 5, then 4n will have both factors 2 and 5, which are required for the product to end with zero.Concluding Solution: Conclude if there is a value of n that satisfies the condition. Yes, if n is any natural number that is a multiple of 5, then 4n will end with the digit zero.

Consider the numbers $4n$ , where $n$ is a natural number. Check whether there is any value of $n$ for which $4n$ ends with the digit zero.

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Consider the numbers 4n4n4n, where nnn is a natural number. Check whether there is any value of nnn for which 4n4n4n ends with the digit zero.

Consider the numbers $4n$ , where $n$ is a natural number. Check whether there is any value of $n$ for which $4n$ ends with the digit zero.