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
2 3 4 5 6 8 9 10 11
128 Yes No Yes No No Yes No No No
990 ........ ........ ........ ........ ........ ........ ........ ........ ........
1586 ........ ........ ........ ........ ........ ........ ........ ........ ........
275 ........ ........ ........ ........ ........ ........ ........ ........ ........
6686 ........ ........ ........ ........ ........ ........ ........ ........ ........
639210 ........ ........ ........ ........ ........ ........ ........ ........ ........
429174 ........ ........ ........ ........ ........ ........ ........ ........ ........
2856 ........ ........ ........ ........ ........ ........ ........ ........ ........
3060 ........ ........ ........ ........ ........ ........ ........ ........ ........
406839 ........ ........ ........ ........ ........ ........ ........ ........ ........

Question

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	........	........	........	........	........	........	........	........	........
429174	........	........	........	........	........	........	........	........	........
2856	........	........	........	........	........	........	........	........	........
3060	........	........	........	........	........	........	........	........	........
406839	........	........	........	........	........	........	........	........	........

Accepted Answer

We know that,Divisibility by 2: If any of the digits 0, 2, 4, 6, or 8 are present in place of the one, the number is divisible by 2.Divisibility by 3: The number is divisible by 3 if the digit sum is a multiple of 3.Divisibility by 4: If the sum of the last two digits, or ones and tens, of a number with 3 or more digits is also divisible by 4, then the number is also divisible by 4.Divisibility by 5: A number is divisible by 5 if its last digit is either 0 or 5.Divisibility by 6: A number is also divisible by 6 if it can be divided by 2 and 3 together.Divisibility by 8: If the sum of the final three digits is a number that can be divided by 8, then the number has 4 or more digits.Divisibility by 9: A number is said to be divisible by 9 if the sum of its digits is also divisible by 9.Divisibility by 10: Any number whose last digit is 0, is divisible by 10.

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