Divisibility Rules Flashcards
A number is divisible by 2 if…?
The last digit is even (0,2,4,6,8).
Examples:
128 is
129 is not
A number is divisible by 3 if…?
The sum of the digits is divisible by 3.
Examples:
381 (3+8+1 = 12, and 12/3 = 4) YES
217 (2+1+7 = 10, AND 10/3 = 3 1/3) NO
A number is divisible by 4 if…?
The last 2 digits are divisible by 4
Examples:
1312 is
(12/4 = 3)
7019 is not
A number is divisible by 5 if…?
The last digit is 0 or 5
175 is
809 is not
A number is divisible by 6 if…?
The number is divisible by 2 and 3
114 (it is even, and 1+1+4 = 6 and 6/3 = 2) Yes
308 (it is even, but 3+0+8 = 11 and 11/3 = 3 2/3) No
A number is divisible by 7 if…?
If you double the last digit and subtract it from the rest of the number and the answer is: 0 or divisible by 7
(Note: you can apply this rule to that answer again if you want)
Examples:
672 (Double 2 is 4, 67-2 = 63, and 63/7 = 9) Yes
905 (Double 5 is 10, 90-10 = 80, and 80/7 = 11 3/7) No
A number is divisible by 8 if … ?
The last three digits are divisible by 8
Examples:
109816
(816/8 = 102) Yes
216302
(302/8 = 37 3/4) No
A number is divisible by 9 if … ?
The sum of the digits is divisible by 9
(Note: you can apply this rule to that answer again if you want)
1629
(1+6+2+9 = 18 and again, 1+8 = 9) Yes
2013
(2+0+1+3 =6) No
A number is divisible by 10 if … ?
The number ends in 0
220 is
221 is not
A number is divisible by 11 if … ?
Add and substract digits in an alternating pattern (add first, subtract second, add third, etc). Then the answer must be:
0 or divisible by 11
1364 : (1-3+6-4 = 0) Yes
913 : (9-1+3 = 11) Yes
3729 : (3-7+2-9 = -11) Yes
987 (9-8+7 = 8) No
A number is divisible by 12 if … ?
The number is divisible by both 3 and 4
Examples:
648
(By 3? 6+4+8 = 18 and 18/3 = 6 Yes. By 4? 48/4 = 12 Yes) Yes
524
(By 3? 5+2+4 = 11, 11/3 = 3 2/3 No. Don’t need to check by 4.) No
