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