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**Divisibility Rules and Finding Factors**

Pre-Algebra Section 4-1

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**Divisibility Rules: What are they?**

Rules to help you determine if numbers are divisible by other numbers. Divisible – if a number can be divided by another number with no remainder, decimal, or fraction. We will learn rules for 2, 3, 4, 5, 6, 8, 9, and 10.

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**Divisibility Rule for 2 A number is divisible by 2 if…**

The number is even. Even numbers end in 2, 4, 6, 8, or 0. Examples 412 230 516

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**Divisibility Rule for 10 A number is divisible by 10 if…**

The number ends in a zero. Examples 4,000 210 50

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**Divisibility Rule for 5 A number is divisible by 5 if…**

The number ends in a 5 or 0. Examples 4,000 215 355

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**Divisibility Rule for 3 A number is divisible by 3 if…**

The sum of the digits of the number is divisible by 3. Examples 354 = 12 12 / 3 = 4 9,363,129 = 33 33/3 = 11

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**Divisibility Rule for 9 A number is divisible by 9 if…**

The sum of the digits of the number is divisible by 9. Examples 495 = 18 18 / 9 = 2 999,918 = 45 45 / 9 = 5

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**Divisibility Rule for 6 A number is divisible by 6 if…**

The number is divisible by both 3 and 2. Examples 930 6000 216

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**Divisibility Rule for 4 A number is divisible by 4 if…**

The last 2 digits of the number is divisible by 4. Examples 9,264 1,209,124 216

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**Divisibility Rule for 8 A number is divisible by 8 if…**

The last 3 digits of the number are divisible by 8. Examples 9,808 8,942,216 848

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**Divisibility Rules A number is divisible by: 2 if the number is even.**

3 if the sum of the digits is divisible by 3. 4 if the last 2 digits of the number are ÷ by 4. 5 if the number ends in a 5 or 0. 6 if the number is divisible by 2 and 3. 8 if the last 3 digits of the number are ÷ by 8. 9 if the sum of the digits is divisible by 9. 10 if the number ends in a 0.

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**What number(s) is the number below divisible by?**

75 3 and 5

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**What number(s) is the number below divisible by?**

111 3

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**What number(s) is the number below divisible by?**

131 None

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**What number(s) is the number below divisible by?**

2,848 2, 4, and 8

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**What number(s) is the number below divisible by?**

9,540 2, 3, 4, 5, 6, 9, and 10

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**What number(s) is the number below divisible by?**

144 2, 3, 4, 6, 8, and 9

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**Factors What is a factor of a number?**

An integer that divides into another integer with a remainder of zero. How can you find a number’s factors? Make an organized list of the all of the problems (multiplication facts) that make that number. 18

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**Listing Factors (Example 1)**

List the positive factors for 54 1 x 54 2 x 27 3 x 18 6 x 9 1, 2, 3, 6, 9, 18, 27, and 54 19

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**Listing Factors (Example 2)**

List the positive factors for 28 1 x 28 2 x 14 4 x 7 1, 2, 4, 7, 14, and 28 20

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**Listing Factors (Example 3)**

List the positive factors for 64 1 x 64 2 x 32 4 x 16 8 x 8 1, 2, 4, 8, 16, 32, and 64 21

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