This document outlines divisibility rules for numbers 2 through 11. It provides the rule for each number, examples of applying each rule, and an exercise for students to practice using the rules to determine which numbers are divisible by each number from 2 to 11. The rules state that a number is divisible by a given number if it meets specific criteria involving its digits, such as having a digit sum or last digit that is a multiple of the number.

1. DIVISIBILITY CRITERIA
Teacher: Moira Clemente Alpresa
IES Maestro Diego Llorente
Los Palacios y Villafranca (Sevilla)
Moira Clemente Alpresa

2. Rule of number 2:
A number is divisible by 2 if its last digit is
either 0 or an even number.
Exercise 1: Find which of the numbers: 239,
300, 675, 570, 800, 495, 888, 6402 and 2088
are multiples of 2.
Solution: 300, 570, 800, 888, 6402 and 2088
Moira Clemente Alpresa

3. Rule of number 3
A number is divisible by 3 if the sum of its
digits is a multiple of 3.
Exercise 2: Find which of the numbers of the
exercise 1 are multiples of 3.
Solution: 300, 675, 570, 495, 888, 6402 and
2088
Moira Clemente Alpresa

4. Rule for number 4
A number is divisible by 4 if its two last digits
are multiples of 4.
Exercise 3: Find which of the numbers of the
exercise 1 are multiples of 4.
Solution: 300, 800, 888 and 2088
Moira Clemente Alpresa

5. Rule for number 5
A number is divisible by 5 if it ends in 0 or 5.
Exercise 4: Find which of the numbers of the
exercise 1 are multiples of 5.
Solution: 300,675, 570, 800 and 495
Moira Clemente Alpresa

6. Rule for number 6
A number is divisible by 6 if it is divisible by 2
and 3.
Exercise 5: Find which of the numbers of the
exercise 1 are multiples of 6.
Solution: 300,570, 888, 6402 and 2088
Moira Clemente Alpresa

7. Rule of number 9
A number is divisible by 9 if the sum of its
digits is a multiple of 9.
Exercise 6: Find which of the numbers of the
exercise 1 are multiples of 9.
Solution: 675, 495 and 2088
Moira Clemente Alpresa

8. Rule of number 10
A number is divisible by 10 if it ends in 0.
Exercise 7: Find which of the numbers of the
exercise 1 are multiples of 10.
Solution: 300, 570 and 800
Moira Clemente Alpresa

9. Rule of number 11
A number is divisible by 11 if the difference
between the sum of the digits on odd
positions and the sum of the digits on even
positions is 0, 11 or a multiple of 11.
Exercise 8: Find which of the numbers of the
exercise 1 are multiples of 11.
Solution: 495 and 6402
Moira Clemente Alpresa

10. Exercise 9
Use the divisibility rules to complete the
following table:
Divisible by
2 3 4 5 6 9 10 11
375
990
1,848
12,300
14,240
Moira Clemente Alpresa

11. Thanks for your attention
Moira Clemente Alpresa