The document discusses divisibility tests for numbers 2 through 11. It provides the rules to determine if a number is divisible by each divisor. For each rule, it gives examples of numbers and determines if they are divisible. It also gives a multiple choice question asking to identify which numbers formed from the digits 7, 2, and 9 are divisible by 3, 6, 9, and 10. It is determined that all 6 numbers are divisible by 3 and 9, and numbers 792 and 972 are divisible by 6.

1.  Shall we start with a game.
 https://www.mathgames.com/skill/7.83-divisibility-
rules

2. DIVISIBILITY TESTS

3. Divisibility test of 2
 The divisibility rule for two states that any number
with the last digit of 0, 2, 4, 6, or 8 will
be divisible by 2.
 Simply put, any even number is divisible by 2.
 If the number is not an even number, it is
not divisible by two.
 Which of the following numbers are divisible by 2.
1. 362
Since the last digit is 2, it is divisible by 2
2. 731
 Since the last digit is 1, it is not divisible by 2

4. Divisibility test of 3
 If the sum of the digits of a number is divisible by 3,
then the number is divisible by 3.
 Which of the following numbers are divisible by 3
1.231-
2+3+1=6
Since 6 is a multiple of 3, 231 is divisible by 3.
2.343-
3+4+3= 10
Since 10 is not a multiple of 3, 343 is not divisible by 3.

5. Divisibility test of 4
 If the last two digits of a whole number
are divisible by 4, then the entire number
is divisible by 4.
 Which of the following numbers are divisible by 4?
a) 132
Since 32 is divisible by 4, 132 is also divisible by 4.
b)72
72 is divisible by 4.
c)382
Since 82 is not divisible by 4, so 382 is not divisible by 4.

6. Divisibility test of 5
 If the last number is either 0 or 5, the entire number
is divisible by 5.
Which of the following numbers are divisible by 5.
a) 375
Since 5 is the last digit, 375 is divisible by 5.
a) 25
Since it ends with 5, 25 is a multiple of 5.
a) 83
since 3 is the last digit, 83 is not divisible by 5.

7. Divisibility test of 6
 For a number to be divisible by 6, it must be divisible by
2 and 3.
 Which of the following numbers are divisible by 6
1. 672
Since the last digit is 2, 672 is divisible by 2
Since the sum of digits is 15, 672 is divisible by 3.
Since 672 is both divisible by 2 and 3, it is divisible by 6.
2. 813
since the last digit is 3, it is not divisible by 2.
Since 813 is not divisible by both 2 and 3, it is not divisible by
6.

8. Divisibility test of 8
 Numbers are divisible by 8 if the number formed by
the last three individual digits is divisible by 8.
 Which of the following numbers are divisible by 8.
1. 328
328 is divisible by 8.
2. 4728
728 is divisible by 8, so 4728 is divisible by 8

9. Divisibility test of 9
 If the sum of the digits of a number is divisible by 9, then the
number is divisible by 9.
 Which of the following numbers are divisible by 9
1.8163-
8+1+6+3=18
Since 18 is divisible by 9, 8163 is also divisible by 9.
2.7214
7+2+1+4=14
Since 14 is not divisible by 9,7214 is not divisible by 9.
3.8353
8+3+5+3=19
Since 19 is n0t divisible by 9, 8353 is also not divisible by 9.

10. Divisibility test of 10
 For a number to be divisible by 10, the last digit must
be a 0.
 1. 29-
Since the last digit is 9, 29 is not divisible by 10.
2. 430-
since the last digit is 0, 430 is divisible by 10.

11. Divisibility test of 11
 A number is divisible by 11, if the difference of the sums of the alternate
digits are either 0 or divisible by 11.
 Which of the following numbers are divisible by 11.
1. 7 1 4 1 2 - 7,4,2 1,1
7+4+2=13
1+1=2
13-2= 11
Since 11 is divisible by 11,71412 is also divisible by 11.
2.376277
3+6+7= 16
7+2+7= 16
16-16=0
376277 is divisible by 11.

12.  4. you are given three digits 7,2 and 9
a. How many three digits can be formed without repeating
any of them.
b. How many of this are divisible by 3?
c. How many of this are divisible by 9?
d. How many of this are divisible by 6?
a. 729 ,792, 279, 297, 972, 927
b. 729, 792, 279,297, 972, 927 (since the sum of all the
numbers are 18, all the numbers are divisible by 3.)
c. 729, 792, 279,297, 972, 927 (since the sum of all the
numbers are 18, all the numbers are divisible by 9.)
d. 792, 972 (since the last digit 2.it is divisible by 2
since the sum is 18,it is divisible by 3
since they are both divisible by 2 and 3, it is also
divisible by 6)