Divisibility Rulesand

Finding Factors

Pre-Algebra

Section 4-1

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.

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

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

Examples412230516

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

The number ends in a zero.

Examples4,00021050

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

The number ends in a 5 or 0.

Examples4,000215355

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

The sum of the digits of the number is divisible by 3.

Examples354

3 + 5 + 4 = 1212 / 3 = 4

9,363,1299 + 3 + 6 + 3 + 1 + 2 + 9 = 33

33/3 = 11

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

The sum of the digits of the number is divisible by 9.

Examples495

4 + 9 + 5 = 1818 / 9 = 2

999,9189 + 9 + 9 + 9 + 1 + 8 = 45

45 / 9 = 5

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

The number is divisible by both 3 and 2.

Examples9306000216

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

The last 2 digits of the number is divisible by 4.

Examples9,264

1,209,124216

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

The last 3 digits of the number are divisible by 8.

Examples9,808

8,942,216848

Divisibility RulesA 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.

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

753 and 5

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

111

3

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

131

None

2,848

2, 4, and 8

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

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

9,540

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

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

144

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

18

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

19

Listing Factors (Example 1)

List the positive factors for 54

19

1 x 54

2 x 27

3 x 18

6 x 9

1, 2, 3, 6, 9, 18, 27, and 54

20

Listing Factors (Example 2)

List the positive factors for 28

20

1 x 28

2 x 14

4 x 7

1, 2, 4, 7, 14, and 28

21

Listing Factors (Example 3)

List the positive factors for 64

21

1 x 64

2 x 32

4 x 16

8 x 8

1, 2, 4, 8, 16, 32, and 64