Number Properties: Divisibility

Question 1

Divisible by 2

Answer 1

Units digit is even: {0, 2, 4, 6, 8}.

Question 2

Divisible by 9

Answer 2

Sum of digits is divisible by 9.

Question 3

Divisible by 3

Answer 3

Sum of digits is divisible by 3.

Question 4

Divisible by 4

Answer 4

2-digit number at the end is divisible by 4. Alternatively, X is a number made up of digits a…bc. If the last 2 digits of the number, bc, mod 4 = 0, then X is divisible by 4. If b is odd, then X is divisible by 4 if c is 2 or 6. If b is even, then X is divisible by 4 if c is 0, 4, or 8.

Question 5

Divisible by 10

Answer 5

Units digit is zero (0).

Question 6

Divisible by 6

Answer 6

The number is divisible by 2 (even) and by 3.

Question 7

Divisible by 5

Answer 7

Units digit is zero (0) or 5.

Question 8

Divisible by 7

Answer 8

X is a number made up of digits a…bc. If (a…b - 2*c) mod 7 = 0 then X is divisible by 7. This process can be applied recursively.

Question 9

Divisible by 8

Answer 9

X is a number made up of digits a…bcd. If the last 3 digits of the number, bcd, mod 8 = 0, then X is divisible by 8. If b is even then, X is divisible by 8 if cd mod 8 = 0. If b is odd then, X is divisible by 8 if (cd - 4) mod 8 = 0.

Question 10

Divisible by 11

Answer 10

Alternating difference/sum is divisible by 11. Alternatively, X is a number made up of digits abcd. If (((a - b) + c) - d) mod 11 = 0, then X is divisible by 11.

Question 11

Divisible by 12

Answer 11

The number is divisible both by 3 and by 4.