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Huda wants to tell Wafaa a number with the product of its digits equal to 24 . What is the sum of the digits of the smallest number that Huda could tell Wafaa?

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Final Answer:

The sum of the digits of the smallest number that Huda could tell Wafaa, with the product of its digits equal to 24, is 11.

Step-by-step explanation:

To find the smallest number with a product of digits equal to 24, we need to consider the prime factorization of 24, which is 2³ * 3. To create the smallest number, we pair the prime factors as closely as possible. Thus, the smallest number is 2³ * 3, which is 24. The sum of the digits in this case is 2 + 4 = 6.

However, the question asks for the smallest number with this property, so we consider the next smallest option, which is 2² * 3 * 1. The sum of the digits in this case is 2 + 2 + 3 + 1 = 8. Continuing to minimize the number, we find that 2 * 3 * 4 = 24, with a sum of digits equal to 2 + 4 = 6. Further reduction by multiplying with 1 gives us 2 * 3 * 4 * 1 = 24, with a sum of digits equal to 2 + 3 + 4 + 1 = 10.

Finally, the smallest number with a product of digits equal to 24 is obtained by multiplying 2 * 3 * 4 * 1 * 1, giving 24, with a sum of digits equal to 2 + 3 + 4 + 1 + 1 = 11. Therefore, the answer is 11.

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