Number Divisible by
2 3 4 5 6 8 9 10 11
128 Yes No Yes No No Yes No No No
990 ... ... ... ... ... ... ... ... ...
1586 ... ... ... ... ... ... ... ... ...
275 ... ... ... ... ... ... ... ... ...
6686 ... ... ... ... ... ... ... ... ...
639210 ... ... ... ... ... ... ... ... ...
429714 ... ... ... ... ... ... ... ... ...
2856 ... ... ... ... ... ... ... ... ...
3060 ... ... ... ... ... ... ... ... ...
406839 ... ... ... ... ... ... ... ... ...
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).

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Solution

Rules of Divisibility:
Divisibility by 2: A number is divisible by 2 if the digit at the unit place is either 0 or multiple of 2
Divisibility by 3: Numbers are divisible by 3 if the sum of all the individual digits is evenly divisible by 3
Divisibility by 4: If the number formed by the last two individual digits is evenly divisible by 4
Divisibility by 5: A number is divisible by 5 if the number's last digit is either 0 or 5.
Divisibility by 6: Numbers are evenly divisible by 6 if they are evenly divisible by both 2 and 3.
Divisibility by 8: Numbers are divisible by 8 if the number formed by the last three individual digits is evenly divisible by 8.
Divisibility by 9: A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9.
Divisibility by 10: A number to be divisible by 10, the last digit must be a 0
Divisibility by 11: We must subtract and then add the digits in an alternating pattern from left to right. If the answer is 0 or 11, then the result is divisible by 11.
Numbers $2$ $3$ $4$ $5$ $6$ $8$ $9$ $10$ $11$
$990$ Yes Yes No Yes Yes No Yes Yes Yes
$1586$ Yes No No No No No No No No
$275$ No No No Yes No No No No Yes
$6686$ Yes No No No No No No No No
$639210$ Yes Yes No Yes Yes No No Yes Yes
$429714$ Yes Yes No No Yes No Yes No No
$2856$ Yes Yes Yes No Yes Yes No No No
$3060$ Yes Yes Yes Yes Yes No Yes Yes No
$406839$ No Yes No No No No No No No

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Question 1

Using divisibility test, 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)

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):

Number	Divisible by
Number	2	3	4	5	6	8	9	10	11
128	Yes	No	Yes	No	No	Yes	No	No	No
990	…	…	…	…	…	…	…	…	…
1586	…	…	…	…	…	…	…	…	…
275	…	…	…	…	…	…	…	…	…
6686	…	…	…	…	…	…	…	…	…
639210	…	…	…	…	…	…	…	…	…
429714	…	…	…	…	…	…	…	…	…
2856	…	…	…	…	…	…	…	…	…
3060	…	…	…	…	…	…	…	…	…
406839	…	…	…	…	…	…	…	…	…

Q. Using divisibility rules , find which of the following numbers are divisible by

2, 5, 10

( say yes or no ) in the given table . What do you observe?

Number	Divisible by $2$	Divisible by $5$	Divisible by $10$
$524$	YES	NO	NO
$1200$
$535$
$836$
$780$
$3500$
$4820$
$48630$

Q. A number is divisible by both 4 and 25. Is it necessary that the number must be divisible by 10. Answer in Yes/ No.

Q. Is seven million ten thousand four hundred thirty two divisible by

8 ?

Answer in Yes/ No.

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Numbers	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$
$990$	Yes	Yes	No	Yes	Yes	No	Yes	Yes	Yes
$1586$	Yes	No	No	No	No	No	No	No	No
$275$	No	No	No	Yes	No	No	No	No	Yes
$6686$	Yes	No	No	No	No	No	No	No	No
$639210$	Yes	Yes	No	Yes	Yes	No	No	Yes	Yes
$429714$	Yes	Yes	No	No	Yes	No	Yes	No	No
$2856$	Yes	Yes	Yes	No	Yes	Yes	No	No	No
$3060$	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	No
$406839$	No	Yes	No	No	No	No	No	No	No