divisibility test of 1 to 10

Dear Student

1) For 1:    Any integer (not a fraction) is divisible by 1

2) For 2: The last digit is even (0,2,4,6,8)

128  Yes

129  No

3) For 3: The sum of the digits is divisible by 3

381 (3+8+1=12, and 12÷3 = 4) Yes

217 (2+1+7=10, and 10÷3 = 3 ¹/₃) No

This rule can be repeated when needed:

99996 (9+9+9+9+6 = 42, then 4+2=6) Yes

4) For 4: 

The last 2 digits are divisible by 4

1312 is (12÷4=3) Yes

7019 is not (19÷4=4 ³/₄) No

We can also subtract 20 as many times as we want before checking:

68: subtract 3 lots of 20 and we get 8 Yes

102: subtract 5 lots of 20 and we get 2 No

Another method is to halve the number twice and see if the result is still a whole number:

124/2 = 62, 62/2 = 31, and 31 is a whole number. Yes

30/2 = 15, 15/2 = 7.5 which is not a whole number. No

5) For 5:

The last digit is 0 or 5

175  Yes

809  No

6) For6:

Is even and is divisible by 3 (it passes both the 2 rule and 3 rule above)

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

7) For7:

Double the last digit and subtract it from a number made by the other digits. The result must be divisible by 7. (We can apply this rule to that answer again)

672 (Double 2 is 4, 67−4=63, and 63÷7=9) Yes

105 (Double 5 is 10, 10−10=0, and 0 is divisible by 7) Yes

905 (Double 5 is 10, 90−10=80, and 80÷7=11 ³/₇) No

8) For8:

The last three digits are divisible by 8

109816 (816÷8=102) Yes

216302 (302÷8=37 ³/₄) No

A quick check is to halve three times and the result is still a whole number:

816/2 = 408, 408/2 = 204, 204/2 = 102 Yes

302/2 = 151, 151/2 = 75.5 No

9) For9:

The sum of the digits is divisible by 9

(Note: This rule can be repeated when needed)

1629 (1+6+2+9=18, and again, 1+8=9) Yes

2013 (2+0+1+3=6) No

10) for 10:
The number ends in 0

220  Yes

221  No