1. Divisibility Rules and Finding Factors
Pre-Algebra
Section 4-1

2. 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.

3. 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

4. Divisibility Rule for 10 A number is divisible by 10 if…
The number ends in a zero.
Examples
4,000
210 50

5. Divisibility Rule for 5 A number is divisible by 5 if…
The number ends in a 5 or 0.
Examples
4,000
215
355

6. 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

7. 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

8. Divisibility Rule for 6 A number is divisible by 6 if…
The number is divisible by both 3 and 2.
Examples
930
6000
216

9. 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

10. 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

11. 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.

12. What number(s) is the number below divisible by?75
3 and 5

13. What number(s) is the number below divisible by?
111 3

14. What number(s) is the number below divisible by?
131
None

15. What number(s) is the number below divisible by?
2,848
2, 4, and 8

16. What number(s) is the number below divisible by?
9,540
2, 3, 4, 5, 6, 9, and 10

17. 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
1 x 54
2 x 27
3 x 18
6 x 9
1, 2, 3, 6, 9, 18, 27, and 54 19

20. 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

21. 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