Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no): 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 6689 639210 429714 2856 3060 406839

Question

Philoid · Accepted Answer

In this question, we have to divide the numbers by the given numbers to see whether it is divisible or not. To check this, we follow the divisibility rules:

(i) For divisible by 2: Any number that has 0,2,4,6, or 8 in its one’s place is divisible by 2.

(ii) For divisible by 3: If the sum of all the digits of the number is multiple of 3, then it is divisible by 3.

(iii) For divisible by 4: Any number whose last two digits (i.e. one’s and ten’s place digits) are divisible by 4 then, the number is divisible by 4.

(iv) For divisible by 5: Any number that has 0 or 5 in its one’s place is divisible by 5.

(v) For divisible by 6: If a number a divisible by both 2 and 3, then it is divisible by 6.

(vi) For divisible by 8: Any number whose last three digits are divisible by 8 then, the number is divisible by 8.

(vii) For divisible by 9: If the sum of all the digits of the number is multiple of 9, then it is divisible by 9.

(viii) For divisible by 10: Any number that has 0 in its one’s place is divisible by 10.

For example-

990

= 990 ÷ 2 = 495 so yes it is divisible.

= 990 ÷ 3 = 330 so yes,

= 990 ÷ 4 = 247.5 which is not completely divisible so no its not divisible by 4,

= 990 ÷ 5 = 198 yes

= 990 ÷ 6 = 165 yes

= 990 ÷ 8 = 123.75 (N0)

= 990 ÷ 9 = 110 yes

= 990 ÷ 10 = 99 yes

= 990 ÷ 11 = 90 yes

Number	Divisible by
Number	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
6689	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

Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no):NumberDivisible by23456891011128YesNoYesNoNoYesNoNoNo9901586275668963921042971428563060406839