Math Course - Divisibility Rules

Refresher Course in Mathematics - Number Theory

Divisibility Rules

Divisibility by	Rule
2	If the number is an even number
3	If the sum of all individual digits in the number is divisible by 3
4	If the last two digits of the number is divisible by 4
5	If the last digit of the number is 0 or 5
6	If the number is even and is divisible by 3
7	Double the last digit. Subtract the doubled last digit from the number without the last digit. If the difference is a multiple of 7, then it is divisible by 7.
8	If the last three digits of the number is divisible by 8
9	If the sum of the individual digits in the number is divisible by 9
10	If the last digit of the number is 0
11	If after subtracting and adding the digits successively the result is divisible by 11

Examples

1) 124 is divisible by 2 since the last digit 4 is divisible by 2.

2) 258 is divisible by 3 since the sum of the digits is 15 (2+5+8=15), and 15 is divisible by 3.

3) 516 is divisible by 4 since 16 is divisible by 4.

4) 395 is divisible by 5 since the last digit is 5.

5) 258 is divisible by 6 since it is divisible by 2 AND it is divisible by 3.

6) 1,603 is divisible by 7, since 160-3(2)=154, 15-4(2)=7, and 7 is divisible by 7.

7) 8,120 is divisible by 8 since 120 is divisible by 8.

8) 549 is divisible by 9 since the sum of the digits is 18 (5+4+9=18), and 18 is divisible by 9.

9) 3,770 is divisible by 10 since the last digit is 0.

10) 9,284 is divisible by 11 since the alternating sum of the digits is 11 (9-2+8-4)


Practice Test - Give it  a try!

1. The number 477 is divisible by each of the following numbers EXCEPT: 3, 6, 9
A. 3
B. 9
C. 6
D. None of the above.

2. The number 348 is divisible by each of the following numbers EXCEPT: 2, 3, 4, 5, 6
A. 6
B. 5
C. 4
D. None of the above.

3. If a number is divisible by 9, then it is also divisible by which number?
A. 2
B. 6
C. 3
D. None of the above.

4. Which number is divisible by 8?
A. 23,624
B. 39,126
C. 120,458
D. None of the above.

5. Which number is divisible by 6?
A. 213
B. 468
C. 621
D. None of the above.