Question

divisibility tests of all numbers?​

Answer 1

The Divisibility Rules

Any integer (not a fraction) is divisible by 1.

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

The sum of the digits is divisible by 3. ...

The last 2 digits are divisible by 4. ...

The last digit is 0 or 5. ...

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

Answer 2

Step-by-step explanation:

#)1

Any integer (not a fraction) is divisible by 1

#)2

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

128 Yes

129 No

#)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

The last 2 digits are divisible by 4

1312 is (12÷4=3) Yes

7019 is not (19÷4=4 3/4) No

A quick check (useful for small numbers) is to halve the number twice and the result is still a whole number.

12/2 = 6, 6/2 = 3, 3 is a whole number. Yes

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

#)5

The last digit is 0 or 5

175 Yes

809 No

#)6

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

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

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

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

The number ends in 0

220 Yes

221 No

#)11

Add and subtract digits in an alternating pattern (add digit, subtract next digit, add next digit, etc). Then check if that answer is 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

#)12

The number is divisible by both 3 and 4 (it passes both the 3 rule and 4 rule above)

648

(By 3? 6+4+8=18 and 18÷3=6 Yes)

(By 4? 48÷4=12 Yes)

Both pass, so Yes

524

(By 3? 5+2+4=11, 11÷3= 3 2/3 No)

(Don't need to check by 4) No

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