Answer:
Explanation:
To find two whole numbers whose product is 10,000 and do not contain the digit zero, we can systematically examine the possible combinations.
The prime factorization of 10,000 is 2^4 * 5^4. We need to find two numbers that can be formed using these prime factors without including the digit zero.
Let's start with the power of 2. The highest power of 2 that can divide 10,000 is 2^4. So, the possible combinations for the power of 2 are 2^0 * 2^4, 2^1 * 2^3, 2^2 * 2^2, 2^3 * 2^1, and 2^4 * 2^0.
For the first combination, 2^0 * 2^4, it results in 1 * 16 = 16. Since 16 contains the digit zero, it doesn't meet the given condition.
Moving on to the next combination, 2^1 * 2^3, we have 2 * 8 = 16. Again, it contains the digit zero.
Continuing with 2^2 * 2^2, we get 4 * 4 = 16. This combination also doesn't satisfy the condition.
Next, we have 2^3 * 2^1, which equals 8 * 2 = 16. As before, it contains the digit zero.
Finally, we have 2^4 * 2^0, which gives us 16 * 1 = 16. Once again, it contains the digit zero.
After examining all the combinations involving powers of 2, we can conclude that there are no suitable combinations that satisfy the given conditions. Therefore, there are no two whole numbers without a zero digit that multiply to give 10,000.