Section 1.1 Patterns in Division
Divisibility Rules
In this unit we will determine the rules for numbers that can be divided by
2, 3, 4, 5, 6, 8, 9 or 10. (When you divide the numbers, the answer is a
whole number...not a decimal)
1. Which of these numbers are divisible (can be divided) by 2? By 5? By 10?
78
27
35
410
→ by 2
→ none
→ by 5
→ by 2,5, and 10
123
2100
4126
795
→ none
→by 2 ,5 and 10
→by 2
→by 5
How do we know a number is divisible by 2? By 5? By 10?
What is the rule?
2:
A number is divisible by 2 if it ends in an EVEN number meaning it
ends in a 0, 2, 4, 6 or 8.
5:
A number is divisible by 5, if it ends in a 5 or 0.
10:
A number is divisible by 10 if it ends in a 0
Investigation
The multiples of 2 are
302
304
308
312
316
320
... All numbers are even
The multiples of 4 are
304
308
312
316
320
324
328
… If a number is divisible by 4 then its also divisible by 2, because 2 is a factor of
4.
*Last two digits are multiples of 4 for the whole number to be divisible by 4.
(301,305 are not divisible even though they go up by 4)
The multiples of 8 are
308
316
324
332
340
348
356
… All numbers has to be divisible by 4 and by 2 because 4 and 2 are multiples of 8.
However 8 is not a factor of 2 and 4 therefore if a number is divisible by 2 and 4
it may not be divisible by 8.
Examples: Which numbers are divisible by 8
2064 (64/8) so yes
1032 by 8
16 by 8
1324 (324/8)
4179 (179/8) so no
15400 yes
72 yes
26394 (394/8) no
So…
A number is divisible by 4 when the last two digits are divisible by 4
A number is divisible by 8 when the last three digits are divisible by 8. Also if
number is divisible by 8 then it has to be divisible by 2 and 4 because 2 and
4 are factors of 8
Complete Pages 8-9 #’s 1, 2, 3, 4, 5
Venn Diagrams
A diagram with overlapping circles to display data.
Example #1
Refer to the following numbers:
2
5
6
40
41
55
315
610
9
65
A) Which numbers are divisible by 2?
2,6,12,32,40,70,98,98,610
B) Which numbers are divisible by 5?
5,25,40,55,65,70,105,315,610
C) Which numbers are divisible by 2 and 5?
40,70,610
D) Which numbers are NOT divisible by 2 or 5?
9,41
E) Create a Venn Diagram to display the results.
12
70
25
98
32
105
9
Divisible by 2
Divisible by 5
2,6,12,32,98
40
70
61
0
9,41
555,5,25,55,65,105,315
9,41
Example #2
Refer to the following numbers:
12
24
35
128
765
1048
56
1482
A) Which numbers are divisible by 5?
35,80,90,765,3960
B) Which numbers are divisible by 8?
24,56,1048,128
C) Which numbers are divisible by 5 and 8?
80,3960
D) Which numbers are NOT divisible by 5 or 8?
12,15019,1482
E) Create a Venn Diagram to display the results.
80
3960
90
15019
Divisible by 5
Divisible by 8
35 35, 90, 765
1
B2
80,
3960
24, 56,
1048,128
12, 1482,
15019
Practice
In your exercise book create a venn diagram to show.....
A) Which of the following numbers are divisible by 4 and 5.
16
97
20
105
33
214
64
216
80
324
95
405
B)Which of the following numbers are divisible by 8 and 10.
115
800
116
928
120
1008
168
1110
450
753
24
35
We can also use a Carroll Diagram to sort numbers.
For Example:
Use the numbers below to complete the Carroll Diagram:
1
47
11
98
15
100
20
Divisible by 2
Not Divisible by 2
Divisible by 5
20,100
15,35
Not Divisible by 5
24,98
1,11,47
Practice
Sort these numbers into the Carroll Diagram below:
17
2632
20
3416
Divisible by 5
Not Divisible by 5
25
94140
1234
2605
Divisible by 4
Not Divisible by 4
20,94140
25,2605
2632,3416
17,1234