To find \(209106 \mod 9\), you can sum the digits of the number and then find the remainder when this sum is divided by 9.

1. Sum the digits of \(209106\):
   \[
   2 + 0 + 9 + 1 + 0 + 6 = 18
   \]

2. Find the modulus:
   \[
   18 \mod 9 = 0
   \]

So, \(209106 \mod 9 = 0\).

Would you like more details or have any questions?

Here are 5 related questions:

1. How can modular arithmetic be used to solve problems in computer science?
2. What does it mean if a number modulo 9 is 0?
3. Can modular arithmetic be used with other bases besides 9?
4. How does modular arithmetic relate to clock arithmetic?
5. What is the Chinese Remainder Theorem and how does it use modular arithmetic?

**Tip:** The method of summing digits to find the modulus 9 is a quick way to check for divisibility by 9. If the sum of the digits is a multiple of 9, so is the original number.

Discover how to calculate the modulus 9 of 209106 using modular arithmetic. Follow a detailed step-by-step solution involving digit summation and modular division. Suitable for Grades 9-12.

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