Demonstrates the divisibility rules for (2, 3, 4, 5, 6, 7, 8, 9, 10, 11) using a number n.
Also demonstrates the divisibility calculator at:
https://www.mathcelebrity.com/divisibility.php
1. Divisibility Rules
● Divisibility means, can we divide by a number, and get an
integer for a result?
● We’ll review rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
1
2. Divisibility Rule for 2
● A number is divisible by 2 if the last digit of the number
ends in (0, 2, 4, 6, 8)
● 120 ← Divisible by 2 since the last digit is 0
● 121← Not divisible by 2 since the last digit is not (0, 2, 4,
6, 8)
2
3. Divisibility Rule for 3
● A number is divisible by 3 if the last digit of the sum of its
digits is divisible by 3
● 375
○ Sum of digits is (3 + 7 + 5) = 15
○ 15/3 = 5 ← Divisible by 3 since the sum of digits is
divisible by 3
● 121
○ ← Not divisible by 3 since the sum of digits is (1 + 2 +
1) = 4. 4/3 = 1.3333 3
4. Divisibility Rule for 4
● A number is divisible by 4 if the number formed by the last
2 digits is divisible by 4
● 120 ← Divisible by 4 since the last 2 digits of 20 divided
by 4 = 5
● 121 ← Not Divisible by 4 since the last 2 digits of 21
divided by 4 = 5.25 which is not an integer
4
5. Divisibility Rule for 5
● A number is divisible by 5 if the last digit of the number
ends in 0 or 5
● 120 ← Divisible by 5 since the last digit is 0
● 121← Not divisible by 5 since the last digit is not 0 or 5
5
6. Divisibility Rules for 6
● A number is divisible by 6 if it is divisible by 2 and divisible
by 3
1. Run the divisibility test for 2
2. Run the divisibility test for 3
3. If (1) passes and (2) passes, then the number is divisible
by 6
6
7. Divisibility Rules for 7
1. Take the last digit of the number you’re testing and double it.
2. Subtract this number from the rest of the digits in the original number.
3. If this new number is either 0 or if it’s a number that’s divisible by 7, then your
number is divisible by 7.
4. If you can’t tell if the new number is divisible by 7, repeat Step 1 with the
smaller number.
5. 245 → Double 5, we get 10. Subtract 24 - 10 = 14 which is divisible by 7
7
8. Divisibility Rules for 8
● A number is divisible by 8 if the number formed by the
last 3 digits is divisible by 8
● 3624
● 624 is divisible by 8 → 78
8
9. Divisibility Rules for 9
● A number is divisible by 9 if the sum of its digits are
divisible by 9
● 342 is divisible by 9 since (3 + 4 + 2) = 9
● 9 is divisible by 9
9
10. Divisibility Rule for 10
● A number is divisible by 10 if the last digit of the number
ends in 0
● 120 ← Divisible by 10 since the last digit is 0
● 121← Not divisible by 10 since the last digit is not 0
10
11. Divisibility Rule for 11
● A number is divisible by 11 either of the following
conditions are true
○ Sum of the odd digits - Sum of the even digits is 0
○ Sum of the odd digits - Sum of the even digits is
divisible by 11
● 121 is divisible by 11 since:
○ Sum of the odd digits (1 + 1)
○ Sum of the even digits is 2
○ Sum of odd digits - Sum of even digits is 2 - 2 = 0 11
