Divisibility Rules
and
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 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
Divisibility Rule for 10
A number is divisible by 10 if…
The number ends in a zero.
Examples
4,000
210
50
Divisibility Rule for 5
A number is divisible by 5 if…
The number ends in a 5 or 0.
Examples
4,000
215
355
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
 3 + 5 + 4 = 12
 12 / 3 = 4
 9,363,129
 9 + 3 + 6 + 3 + 1 + 2 + 9 = 33
 33/3 = 11
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
 4 + 9 + 5 = 18
 18 / 9 = 2
 999,918
 9 + 9 + 9 + 9 + 1 + 8 = 45
 45 / 9 = 5
Divisibility Rule for 6
A number is divisible by 6 if…
The number is divisible by both 3 and 2.
Examples
930
6000
216
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
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
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.
What number(s) is the number below
divisible by?
75
3 and 5
What number(s) is the number below
divisible by?
111
3
What number(s) is the number below
divisible by?
131
None
What number(s) is the number below
divisible by?
2,848
2, 4, and 8
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
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.
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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
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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
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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
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