Divisibility Rules
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Transcript Divisibility Rules
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.
18
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
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
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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