Using divisibility tests, determine which of the following numbers are divisible by $ 2$; by $ 3$; by$ 4$; by $ 5$; by$ 6$; by $ 8$; by $ 9$; by $ 10$; by $ 11$ (say, yes or no):
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline \multicolumn{1}{|c|}{} & \multicolumn{6}{c|}{ Divisible By } \\
\hline Numbers & 2 & 3 & 4 & 5 & 6 & 8 & 9 & 10 & 11 \\
\hline 128 & Yes & No & No & Yes & No & No & Yes & No & No \\
\hline 990 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\
\hline 1586 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\
\hline 275 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\
\hline 6686 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\
\hline 639210 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\
\hline 429714 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\
\hline 2856 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\
\hline 3060 & \( -589 \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\
\hline
\end{tabular}
Using divisibility tests, determine which of the following numbers are divisible by $ 2$; by $ 3$; by$ 4$; by $ 5$; by$ 6$; by $ 8$; by $ 9$; by $ 10$; by $ 11$ (say, yes or no):
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline \multicolumn{1}{|c|}{} & \multicolumn{6}{c|}{ Divisible By } \\ \hline Numbers & 2 & 3 & 4 & 5 & 6 & 8 & 9 & 10 & 11 \\ \hline 128 & Yes & No & No & Yes & No & No & Yes & No & No \\ \hline 990 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\ \hline 1586 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\ \hline 275 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\ \hline 6686 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\ \hline 639210 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\ \hline 429714 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\ \hline 2856 & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\ \hline 3060 & \( -589 \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) & \( -- \) \\ \hline \end{tabular}
Rules for divisibility :
- Divisibility Rule of
If a number is even or a number whose last digit is an even number i.e. ,,, including , it is always completely divisible by .
- Divisibility Rules for
Divisibility rule for states that a number is completely divisible by if the sum of its digits is divisible by .
- Divisibility Rule of
If the last two digits of a number are divisible by , then that number is a multiple of and is divisible by completely.
- Divisibility Rule of
Numbers, which last with digits, 0 or are always divisible by .
- Divisibility Rule of
Numbers which are divisible by both and are divisible by That is, if the last digit of the given number is even and the sum of its digits is a multiple of , then the given number is also a multiple of .
- Divisibility Rules for
The rule for divisibility by is a bit complicated which can be understood by the steps given below:
- Divisibility Rule of
If the last three digits of a number are divisible by , then the number is completely divisible by .
- Divisibility Rule of
The rule for divisibility by is similar to divisibility rule for . That is, if the sum of digits of the number is divisible by , then the number itself is divisible by .
- Divisibility Rule of
Divisibility rule for states that any number whose last digit is , is divisible by .
- Divisibility Rules for
If the difference of the sum of alternative digits of a number is divisible by , then that number is divisible by completely.
Hence, the required complete table is:
Rules for divisibility :
- Divisibility Rule of
If a number is even or a number whose last digit is an even number i.e. ,,, including , it is always completely divisible by .
- Divisibility Rules for
Divisibility rule for states that a number is completely divisible by if the sum of its digits is divisible by .
- Divisibility Rule of
If the last two digits of a number are divisible by , then that number is a multiple of and is divisible by completely.
- Divisibility Rule of
Numbers, which last with digits, 0 or are always divisible by .
- Divisibility Rule of
Numbers which are divisible by both and are divisible by That is, if the last digit of the given number is even and the sum of its digits is a multiple of , then the given number is also a multiple of .
- Divisibility Rules for
The rule for divisibility by is a bit complicated which can be understood by the steps given below:
- Divisibility Rule of
If the last three digits of a number are divisible by , then the number is completely divisible by .
- Divisibility Rule of
The rule for divisibility by is similar to divisibility rule for . That is, if the sum of digits of the number is divisible by , then the number itself is divisible by .
- Divisibility Rule of
Divisibility rule for states that any number whose last digit is , is divisible by .
- Divisibility Rules for
If the difference of the sum of alternative digits of a number is divisible by , then that number is divisible by completely.
Hence, the required complete table is:
