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```Factors and Divisibility
Copy the following numbers and chart into your notebook.
22
120
333
52
135
999
Test Number
22
52
122
152
156
222
252
256
20
7984
120
135
530
730
820
835
984
321
35
1984
333
999
122
530
0
152
730
1
156
820
2
222
835
3
252
984
256
321
Divisor
4
5
6
20
35
7
7984
1984
8
9
10
Activity:
For each of the following numbers, determine the divisibility rule (or
Pattern that tells you if a number can be divided by it)
0
1
2
3
4
5
6
7
8
9
10
Divisible Rules
0
No number is divisible by 0. If a number is divided by 0, it is called undefined (you will
1
All numbers are divisible by 1. All numbers are actually understood to be over 1, but we
just do not write it.
2
All even numbers are divisible by 2. If the number ends in 0, 2, 4, 6, or 8, then it is
divisible by 2
3
If the sum of the digits (digital root) of the number is divisible by 3, then the entire number
is divisible by 3. For example, 7392 = 7 + 3 + 9 + 2 = 21. Since 21 is divisible by 3, then
7392 is divisible by 3.
4
If the last two digits are divisible by 4 then the entire number is divisible by 4. For
example, 8316. Since the last 2 digits are 16 and 16 is divisible by 4, then 8316 is
divisible by 4.
5
All numbers that end in a 0 or a 5 are divisible by 5.
6
If a number is divisible by 3 and is an even number (which means that it is divisible by 2),
then it is divisible by 6.
7
There is NO rule for determining if a number is divisible by 7.
8
If the last 3 digits of a number is divisible by 8, then the number is divisible by 8. For
example, 23,848. Since the last 3 digits of 848 is divisible by 8, then 23,848 is divisible
by 8
9
If the sum of the digits (digital root) of the number is divisible by 9, then the entire number
is divisible by 9.
For example, 76,347 = 7 + 6 + 3 + 4 + 7 = 27. Since 27 is divisible by 9, then 76, 347 is
also divisible by 9.
All numbers that end in a 0 are divisible by 10.
10
Digital Root: when you add up all of the individual digits of a number and you continue doing
this until you end up with a single digit number.
For Example: 76,233
7+6+2+3+3
= 21
=2+1
=3
Therefore, the digital root of 76,233 is 3. This also means that 76, 233 is
divisible by 3.
Prime Number:
a number that only has two factors, 1 and itself.
For Example:
7
23
The factors of 7 are 1 and 7
The factors of 23 are 1 and 23
```
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