Part D: Explain the Rule

Write the divisibility rule for each number below.

Rule for 2:

Rule for 5:

Rule for 10:

Rule for 3:

Rule for 9:

Rule for 11:

***Bonus Challenge

Find a number that is divisible by all six rules (2, 5, 10, 3, 9, and 11). Explain why it works.

Answer:

Explanation:

The divisibility rules help identify whether numbers can be divided evenly by 2, 3, 5, 9, 10, and 11 based on their last digits or sums of digits. A number like 990 is divisible by all six rules because it meets the criteria for each. This means it has specific digit properties that align with each divisibility rule.
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Answered by Anonymous | 2025-07-04

Here's a breakdown of the divisibility rules for each of the numbers:
Rule for 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8).
Rule for 5: A number is divisible by 5 if its last digit is either 0 or 5.
Rule for 10: A number is divisible by 10 if its last digit is 0.
Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
Rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Rule for 11: A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is divisible by 11.
Bonus Challenge
Find a number that is divisible by 2, 5, 10, 3, 9, and 11. To solve this, we need a number that meets all these criteria:

Divisible by 2, 5, and 10: It must end in 0.
Divisible by 3 and 9: The sum of its digits must be divisible by 9 (which means also by 3).
Divisible by 11: The alternating sum of its digits must be divisible by 11.

A well-known number that satisfies being divisible by all of these is 990:

It ends in 0 (divisible by 2, 5, and 10).
The sum of its digits (9 + 9 + 0 = 18) is divisible by 9 (and thus 3).
The alternating sum of its digits (9 - 9 + 0 = 0) is divisible by 11.

Thus, 990 works because it meets all the divisibility rules listed above.

Answered by RyanHarmon181 | 2025-07-06