If AxB=1,000,000 what is A+B but both of the numbers can’t have a 0 in them

To solve for \( A + B \) given \( A \times B = 1,000,000 \) with the condition that neither \( A \) nor \( B \) can contain the digit 0, we need to find pairs \((A, B)\) that multiply to 1,000,000 and meet this condition.

### Factorization of 1,000,000

First, factorize 1,000,000:
\[ 1,000,000 = 10^6 = (2 \times 5)^6 = 2^6 \times 5^6 \]

Next, we seek combinations of \( A \) and \( B \) using these factors, ensuring neither number contains the digit 0.

### Possible Values for \( A \) and \( B \)

One way to proceed is by trial and error or logical reasoning with known digit constraints.

Let's explore combinations:

- Since \( 2^6 = 64 \) and \( 5^6 = 15625 \), we need to find a pair where both numbers multiply to \( 1,000,000 \) without any digit being 0.

#### Trying \( A = 128 \times 3906 \)

1. \( 128 \times 78125 \): Here \( 128 \) and \( 78125 \) contain 0.

#### Trying \( 3125 \times 320 \)

2. \( 3125 \times 320 \): Again, 320 has 0.

To avoid combinations involving digits '0', we further need other combinations:

\((256, 3906)\)

### Correct Combination

1. \( 256 \times 3906 = 1,000,000 \)
2. Checking digits:
   - 256 does not contain 0
   - 3906 does not contain 0

### Sum

Thus, \( A = 256 \) and \( B = 3906 \), so:
\[ A + B = 256 + 3906 = 4162 \]

### Conclusion
\[ A + B = 4162 \]

Would you like more details or have any questions about this solution?

Here are some questions you might find interesting:
1. How do you handle factorization of large numbers?
2. Can you explain why certain pairs of factors were ruled out?
3. What is the importance of digit constraints in such problems?
4. How can we ensure that a pair meets the criteria without trial and error?
5. What are some methods to check if a number contains a specific digit?

**Tip:** When solving similar problems, consider using prime factorization to find potential pairs and then apply any specific constraints.

Explore how to solve for A + B given AxB = 1,000,000 with the constraint that neither A nor B can have the digit 0. This problem involves factorization, multiplication strategies, and handling digit constraints in mathematical equations. Suitable for advanced high school or college-level students.

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