Divisibility Rules Reference Sheet & Poster - Kraus Math - Free Printable

The image you provided is a colorful reference sheet and poster for Divisibility Rules. These rules help determine whether a number is divisible by another number without performing actual division. Below, I will explain each rule listed in the image:

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Divisibility Rules

#### 1. Divisible by 2
- Rule: The last digit of the number is even.
- Explanation: A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.
- Example:
- 597,314 (last digit is 4, which is even) → divisible by 2.
- 39,958 (last digit is 8, which is even) → divisible by 2.

#### 2. Divisible by 3
- Rule: The sum of all the digits of the number is divisible by 3.
- Explanation: Add up all the digits of the number. If the sum is divisible by 3, then the original number is divisible by 3.
- Example:
- 12,593,751 → \(1 + 2 + 5 + 9 + 3 + 7 + 5 + 1 = 33\), and 33 is divisible by 3 → divisible by 3.
- 33 → \(3 + 3 = 6\), and 6 is divisible by 3 → divisible by 3.

#### 3. Divisible by 4
- Rule: The last two digits of the number are divisible by 4.
- Explanation: Look at the last two digits of the number. If they form a number divisible by 4, then the original number is divisible by 4.
- Example:
- 23,504 → The last two digits are 04, and 4 is divisible by 4 → divisible by 4.
- 4 → divisible by 4.

#### 4. Divisible by 5
- Rule: The last digit of the number is either 0 or 5.
- Explanation: A number is divisible by 5 if its last digit is 0 or 5.
- Example:
- 78,923,475 (last digit is 5) → divisible by 5.
- 6,337,890 (last digit is 0) → divisible by 5.

#### 5. Divisible by 6
- Rule: The number is divisible by both 2 and 3.
- Explanation: A number is divisible by 6 if it satisfies the divisibility rules for both 2 and 3.
- Example:
- 29,423,136:
- Last digit is 6 (even) → divisible by 2.
- Sum of digits: \(2 + 9 + 4 + 2 + 3 + 1 + 3 + 6 = 30\), and 30 is divisible by 3 → divisible by 3.
- Since it passes both tests, it is divisible by 6.

#### 6. Divisible by 8
- Rule: The last three digits of the number are divisible by 8.
- Explanation: Look at the last three digits of the number. If they form a number divisible by 8, then the original number is divisible by 8.
- Example:
- 62,123,572,816 → The last three digits are 816, and 816 is divisible by 8 → divisible by 8.
- 816 → divisible by 8.

#### 7. Divisible by 9
- Rule: The sum of all the digits of the number is divisible by 9.
- Explanation: Add up all the digits of the number. If the sum is divisible by 9, then the original number is divisible by 9.
- Example:
- 113,583,420 → \(1 + 1 + 3 + 5 + 8 + 3 + 4 + 2 + 0 = 27\), and 27 is divisible by 9 → divisible by 9.
- 27 → divisible by 9.

#### 8. Divisible by 10
- Rule: The last digit of the number is zero.
- Explanation: A number is divisible by 10 if its last digit is 0.
- Example:
- 47,339,860 (last digit is 0) → divisible by 10.
- 0.987,400 (last digit is 0) → divisible by 10.

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Summary

These rules provide quick methods to check divisibility without performing long division. Each rule is designed to simplify the process based on specific patterns in the digits of the number.

If you have any specific numbers you want to test for divisibility, feel free to ask!

Final Answer:
\boxed{\text{See explanations above for each divisibility rule.}}