Question

(iv) 2856
(v) 1838
2. Using the divisibility test, determine which of the
following numbers are divisible by 4 and by 8.
(i) 512
(ii) 12154 (iii) 19540
(iv) 1832 (v) 1925620 (vi) 256653000
3. Using the divisibility test, determine which of the
following numbers are divisible by 3 and by 9.
(i) 35433 (ii) 60902 (iii) 5247
(iv) 37917 (v) 52776 (vi) 872645
4. Using the divisibility test, determine which of the
following numbers are divisible by 11.
(i) 121
(ii) 10241 (iii) 18183
(iv) 3278965 (v) 201853
(vi) 9418629​

Answer 1

A positive integer NN is divisible by

\color{#20A900}{\boxed{\mathbf{2}}}  

2

​  

 if the last digit of NN is 2, 4, 6, 8, or 0;

\color{#20A900}{\boxed{\mathbf{3}}}  

3

​  

 if the sum of digits of NN is a multiple of 3;

\color{#20A900}{\boxed{\mathbf{4}}}  

4

​  

 if the last 2 digits of NN are a multiple of 4;

\color{#20A900}{\boxed{\mathbf{5}}}  

5

​  

 if the last digit of NN is either 0 or 5;

\color{#20A900}{\boxed{\mathbf{6}}}  

6

​  

 if NN is divisible by both 2 and 3;

\color{#20A900}{\boxed{\mathbf{7}}}  

7

​  

 if subtracting twice the last digit of NN from the remaining digits gives a multiple of 7 (e.g. 658 is divisible by 7 because 65 - 2 x 8 = 49, which is a multiple of 7);

\color{#20A900}{\boxed{\mathbf{8}}}  

8

​  

 if the last 3 digits of NN are a multiple of 8;

\color{#20A900}{\boxed{\mathbf{9}}}  

9

​  

 if the sum of digits of NN is a multiple of 9;

\color{#20A900}{\boxed{\mathbf{10}}}  

10

​  

 if the last digit of NN is 0;

\color{#20A900}{\boxed{\mathbf{11}}}  

11

​  

 if the difference of the alternating sum of digits of NN is a multiple of 11 (e.g. 2343 is divisible by 11 because 2 - 3 + 4 - 3 = 0, which is a multiple of 11);

\color{#20A900}{\boxed{\mathbf{12}}}  

12

​  

 if NN is divisible by both 3 and 4.