# divisibility test of 1 to 10

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)

12**8** **Yes**

12**9** **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**

The last 2 digits are divisible by 4

13**12** is (12÷4=3) **Yes**

70**19** 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**

The last digit is 0 or 5

17**5** **Yes**

80**9** **No**

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**

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**

The last three digits are divisible by 8

109**816** (816÷8=102) **Yes**

216**302** (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

22**0** **Yes**

22**1** **No**

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